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A Speculative Grammar for Knowledge Bases

AI3:::Adaptive Information (Mike Bergman) - Mon, 06/20/2016 - 17:35

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Finding a Natural Classification to Support AI and Machine Learning

Effective use of knowledge bases (KBs) for artificial intelligence (AI) would benefit from a definition and organization of KB concepts and relationships specific to those AI purposes. Like any language, the construction of logical statements within KBAI (knowledge-based artificial intelligence) requires basic primitives for how to express these arguments. Just as in human language where we split our words into roughly nouns and verbs and modifiers and conjunctions of the same, we need a similar primitive vocabulary and basic rules of statement construction to actually begin this process. In all language variants, these basic building blocks are known as the grammar of the language. A well-considered grammar is the first step to being able to construct meaningful and coherent statements about our knowledge bases. The context for how to construct this meaningful grammar needs to be viewed through the lens of the KB’s purpose, which, in our specific case, is for artificial intelligence and machine learning.

In one of my recent major articles I discussed Charles Sanders Peirce and his ideas of the three universal categories and their relation to semiosis [1]. We particularly focused on how Peirce approached categorization and its basis in his logic of semiosis. I’d like to restrict and deepen that discussion a bit, now concentrating on what Peirce called the speculative grammar, the starting point and Firstness of his overall method.

The basic idea of the speculative grammar is simple. What are the vocabulary and relationships that may be involved in the understanding of the question or concept at hand? What is the “grammar” for the question at hand that may help guide how to increase our understanding of it? What are the concepts and terms and relationships that populate our domain of inquiry?

Hearing the term ‘semiosis’ in relation to Peirce most often brings to mind his theory of signs. But for Peirce semiosis was a broader construct still, representing his overall theory of logic and truth-testing. Signs, symbols and representation were but the first part of this theory, the ‘Firstness’ or speculative grammar about how to formulate and analyze logic.

Though he provides his own unique take on it, Peirce’s idea of speculative grammar, which he erroneously ascribed to Duns Scotus, can actually be traced back to the 1300s and the writings of Thomas of Erfurt, one of the so-called Modists of the medieval philosophers [2]. Here is how Peirce in his own words placed speculative grammar in relation to his theory of logic [3]:

“All thought being performed by means of signs, logic may be regarded as the science of the general laws of signs. It has three branches: (1) Speculative Grammar, or the general theory of the nature and meanings of signs, whether they be icons, indices, or symbols; (2) Critic, which classifies arguments and determines the validity and degree of force of each kind; (3) Methodeutic, which studies the methods that ought to be pursued in the investigation, in the exposition, and in the application of truth.” (CP 2:260)

Speculative grammar is thus a Firstness in Peirce’s category structure, with logic methods being a Secondness and the process of logic inquiry, the methodeutic, being a Thirdness.

Still, What Exactly is a Speculative Grammar?

Charles S. Peirce’s view of logic was that it was a formalization of signs, what he termed semiosis. As stated, three legs provide the basis of this formal logic. The first leg is a speculative grammar, in which one strives to capture the signs that most meaningfully and naturally describe the current domain of discourse. The second leg is the means of logical inference, be it deductive, inductive or abductive (hypothesis generating). The third leg is the method or process of inquiry, what came to be known from Perice and others as pragmaticism. The methods of research or science, including the scientific method, result from the application of this logic. The “pragmatic” part arises from how to select what is important and economically viable to investigate among multiple hypotheses.

In Peirce’s universal categories, Firstness is meant to capture the potentialities of the domain at hand, the speculative grammar; Secondness is meant to capture the particular facts or real things of the domain at hand, the critic; and Thirdness is meant to capture methods for discovering the generalities, laws or emergents within the domain, the methodeutic. This mindset can really be applied to any topic, from signs themselves to logic and to science [1]. The “surprising fact” or new insight arising from Thirdness points to potentially new topics that may themselves become new targets for this logic of semiosis.

In its most general sense, Peirce describes this process or method of discovery and explication of new topics as follows [3]:

“. . . introduce the monadic idea of »first« at the very outset. To get at the idea of a monad, and especially to make it an accurate and clear conception, it is necessary to begin with the idea of a triad and find the monad-idea involved in it. But this is only a scaffolding necessary during the process of constructing the conception. When the conception has been constructed, the scaffolding may be removed, and the monad-idea will be there in all its abstract perfection. According to the path here pursued from monad to triad, from monadic triads to triadic triads, etc., we do not progress by logical involution — we do not say the monad involves a dyad — but we pursue a path of evolution. That is to say, we say that to carry out and perfect the monad, we need next a dyad. This seems to be a vague method when stated in general terms; but in each case, it turns out that deep study of each conception in all its features brings a clear perception that precisely a given next conception is called for.” (CP 1.490)

The ideas of Firstness, Secondness and Thirdness in Peirce’s universal categories are not intended to be either sequential or additive. Rather, each interacts with the others in a triadic whole. Each alone is needed, and each is irreducible.

As Peirce says in his Logic of Relatives paper [4]:

“The fundamental principles of formal logic are not properly axioms, but definitions and divisions; and the only facts which it contains relate to the identity of the conceptions resulting from those processes with certain familiar ones.” (CP 3.149)

Without the right concepts, terminology, or bounding — that is, the speculative grammar — it is clearly impossible to properly understand or compose the objects or Secondness that populate the domain at hand. Without the right language and concepts to capture the connections and implications of the domain at hand — again, part of its speculative grammar — it is not possible to discover the generalities or the “surprising fact” or Thirdness of the domain.

The speculative grammar is thus needed to provide the right constructs for describing, analyzing, and reasoning over the given domain. Our logic and ability to understand the focus of our inquiry requires that we describe and characterize the domain of discourse in ways that are properly scoped and related. How well we bound, characterize and signify our problem domains — that is, the speculative grammar — directly relates to how well we can reason and inquire over that space. It very much matters how we describe, relate and define what we analyze and manipulate.

Let’s take a couple of examples to illustrate this. First, imagine van Leeuwenhoek first discovering “animacules” under his early, advanced microscopes. New terms and concepts like flagella, cells, and vacuoles needed to be coined and systematized in order for further advances in microorganisms to be described. Or, second, imagine “action at a distance” phenomena such as magnetic repulsion or static electricity causing hair to stand on end. For centuries these phenomena were assumed to be caused by atomistic particles too small to see or discover. Only when Hertz was able to prove Maxwell‘s equations of electromagnetism hundreds of years later in the mid-1800s were the concepts and vocabulary of waves and fields sufficiently developed to begin to unravel electromagnetic theory in earnest. Progress required the right concepts and terminology.

For Peirce, the triadic nature of the sign — and its relation between the sign, its object and its interpretant — was the speculative grammar breakthrough that then allowed him to better describe the process of signmaking and its role in the logic of inquiry and truth-testing (semiosis). Because he recognized it in his own work, Peirce understood a conceptual “grammar” appropriate to the inquiry at hand is essential to further discovery and validation.

How Might a Speculative Grammar Apply to Knowledge Bases?

Perhaps one way to understand what is intended by a speculative grammar is to define one. In this instance, let’s aim high and posit a grammar for knowledge bases.

Since we had been moving steadily to a typology design for our entities and were looking at all other aspects of structure and organization of the knowledge base (KB) [5], we decided to apply this idea of a speculative grammar to the quest. We consciously chose to do this from two perspectives. First, in keeping with Peirce’s sign trichotomy, we wanted to keep the interpretant of an agent doing artificial intelligence front-and-center. This meant that the evaluative lens we wanted to apply to how we conceptualized, organized and provided a vocabulary for the knowledge space was to be done from the viewpoint of machine learning and its requirements. Once we posit the intelligent agent as the interpretant, the importance of a rich vocabulary and text (NLP), a well-formed structure and hierarchy (logical inference), and a rich feature set (structure and coherent characterizations), becomes clear.

Second, we wanted to look at the basis for organizing the KB concepts into the Peircean mindset of Firstness (potentials), Secondness (particulars) and Thirdness (generals). Our hypothesis was that conforming to Peirce’s trichotomous splits would help guide us in deciding the myriad possibilities of how to arrange and structure a knowledge base.

We looked as well as to what language to write these specifications. Our current languages of RDF, SKOS and OWL could capture all first-order logic imperatives, but the OWL annotation, object and datatype properties did not exactly conform to the splits we saw [11]. On the other hand, tooling such as Protégé and the OWL API were immensely helpful, and there are quite a few supporting tools. Formalisms like conceptual graphs were richer and handled higher-order logics, but also lacked tooling and widespread use. Since we knew we could adapt to OWL, we stuck with our original language set.

Guarino, in some of the earliest (1992) writings leading to semantic technologies, had posited knowledge bases split into concepts, attributes and relations [6]. This was close to our thinking, and provided comfort that such splits were also being considered from the earliest days of the semantic Web. Besides Peirce, we studied many philosophers across history regarding fundamental concepts in knowledge organization. Aristotle’s categories were influential, and have mostly stood the test of time and figured prominently in our thinking. We also reviewed efforts such as Sarbo’s to apply Peirce to knowledge bases [7], as well as most other approaches claiming Peirce in relation to KBs that we could discover [8-10].

Because the intent was to create a feature-rich logic machine for AI, we of course wanted the resulting system to be coherent, sound, consistent, and relatively complete. Though the intended interpretant is artificial agents, training them and vetting results still must be overseen by humans in order to ensure quality. We thus wanted all features and structural aspects to be described and labeled sufficiently to be understood and interpreted by humans. These aspects further had to be suitable for direct translation into any human language. For interchange purposes, we try to use canonical forms.

Once these preliminaries are out of the way, the task at hand can finally focus on the fundamental divisions within the knowledge base. In accordance with the Peircean categories, we saw these splits:

  • Firstness — these ‘potentials’ include base concepts, attributes, and relations in the abstract
  • Secondness — these are the ‘particular’ things in the domain, including entities, events and activities
  • Thirdness — the ‘generals’ in the knowledge base include classes, types, topics and processes.

Ultimately, features richness was felt to be of overriding importance, with features explicitly understood to include structure and text.

A Speculative Grammar for Knowledge Bases

With these considerations in mind, we are now able to define the basic vocabulary of our knowledge base, one of the first components of the speculative grammar. This base vocabulary is:

  • Attributes are the ways to characterize the entities or things within the knowledge base; while the attribute values and options may be quite complex, the relationship is monadic to the subject at hand. These are intensional properties of the subject
  • Relations are the way we describe connections between two or more things; relations are external-facing, between the subject and another entity or concept; relations set the extensional structure of the knowledge graph [11]
  • Entities are the basic, real things in our domain of interest; they are nameable things or ideas that have identity, are defined in some manner, can be referenced, and should be related to types; entities are the bulk of the overall knowledge base
  • Events are nameable sequences of time, are described in some manner, can be referenced, and may be related to other time sequences or types
  • Activities are sustained actions over durations of time; activities may be organized into natural classes
  • Types are the hierarchical classification of natural kinds within all of the terms above
  • The Typology structure is not only a natural organization of natural classes, but it enables flexible interaction points with inferencing across its ‘accordion-like’ design (see further [5])
  • Base concepts are the vocabulary to the grammar and top-level concepts in the knowledge graph, organized according to Peircean-informed categories
  • Annotations are indexes and the metadata of the KB; these can not be inferenced over. But, they can be searched and language features can be processed in other ways.

How these vocabulary terms relate to one another and the overall knowledge base is shown by this diagram:

A Knowledge Base Grammar

As part of the ongoing simplification of the TBox [12], we need to be able to distinguish and rationalize the various typologies used in the system: attributes, relations, entities, events and activities. Here are some starting rules:

  • RULE: Entities can not be topics or types
  • RULE: Entities are not data types; these are handled under values processing
  • RULE: Events are like entities, except they have a discrete time beginning and end; they may be nameable
  • RULE: Activities (or actions) act upon entities, but do not require a discrete time beginning or end
  • RULE: Attributes are not metadata; they are characteristics or descriptors of an entity
  • RULE: Topics or base concepts do not have attributes
  • RULE: Entity types have the attributes of all type members
  • RULE: Relation types do not have attributes (also, relations do not have attributes)
  • RULE: Attribute types do not have attributes (also, attributes do not have attributes)
  • RULE: All types may have hierarchy
  • RULE: No attributes are provided on relations (as in E-R modeling), just annotations
  • RULE: Annotations are not typed, and can not be inferred over.

As we work further with this structure, we will continue to add to and refine these governing rules.

The columns in the figure above also roughly correspond to Peirce’s three universal categories. The first column and part of the second (attributes and relations) correspond to Firstness; the remainder of the second column corresponds to Secondness; and the third column corresponds to Thirdness. I’ll discuss these distinctions further in a later article.

In combination, this vocabulary and rules set, as allocated to Peirce’s categories, constitutes the current speculative grammar for our knowledge bases.

Recall that the interpretants for this design are artificial agents. It is unclear how the resulting structure will be embraced by humans, since we were not the guiding interpretant. But, like being able to readily discern whether an object is plumb or level, humans have the ability to recognize adaptive structure. I think what we are building here will therefore withstand scrutiny and be useful to all intelligent agents, artificial or human.

Conclusion

Generating new ideas and testing the truth of them is a logical process that can be formalized. Critical to this process is the proper bounding, definition and vocabulary upon which to conduct the inquiries. As Charles Peirce argued, the potentials central to the inquiries for a given topic need to be expressed through a suitable speculative grammar to make these inquiries productive. How we think about, organize and define our problem spaces is central to that process.

The guiding lens for how we do this thinking comes from the purpose or nature of the inquiries at hand. In the case of machine learning applied to knowledge bases, this lens, I have argued, needs to be grounded in Peirce’s categories of Firstness, Secondness and Thirdness, all geared to feature generation upon which machine learners may operate. The structure of the system should also be geared to enable (relatively quick and cheap) creation of positive and negative training sets upon which to train the learners. In the end, the nature of how to structure and define knowledge bases depends upon the uses we intend them to fulfill.

[1] M.K. Bergman, 2016. “A Foundational Mindset: Firstness, Secondness, Thirdness,” AI3:::Adaptive Information blog, March 21, 2016. [2] Alessandro Isnenghi, 2008. “A Semiótica de CS Peirce e a Gramática Especulativa de Modistae” (or, “C.S. Peirce’s Semiotic And Modistae’s Grammatica Speculativa“), Cognitio-Estudos: revista eletrônica de filosofia. ISSN 1809-8428 5, no. 2 (2008). [3] See the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208. [4]  This quote is drawn from Charles Sanders Peirce, 1870. “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9 (1870), 317–378 (the “Logic of Relatives”), using the same numbering as from [3]. [5] M.K. Bergman, 2016. “Rationales for Typology Designs in Knowledge Bases,” AI3:::Adaptive Information blog, June 6, 2016. [6] Nicola Guarino, 1992. “Concepts, Attributes and Arbitrary Relations: Some Linguistic and Ontological Criteria for Structuring Knowledge Bases.” Data & Knowledge Engineering 8, no. 3 (1992): 249-261. Continuing in the same vein, see also Nicola Guarino, 1997. “Some Organizing Principles for a Unified Top-level Ontology,” in AAAI Spring Symposium on Ontological Engineering, pp. 57-63. 1997. Also, for a general view of ontology at that time, see Thomas R. Gruber, 1993. “A Translation Approach to Portable Ontology Specifications.” Knowledge Acquisition 5, no. 2 (1993): 199-220. [7] Auke JJ Van Breemen and Janos J. Sarbo, 2009. “The machine in the ghost: The syntax of mind.” Signs-International Journal of Semiotics 3 (2009): 135-184. and Janos J. Sarbo and József I. Farkas, 2002. “On the isomorphism of signs, logic and language.” [8] Lehmann, Fritz, and Rudolf Wille. “A triadic approach to formal concept analysis“. Springer Berlin Heidelberg, 1995. [9] József István Farkas, 2008. “A Semiotically Oriented Cognitive Model of Knowledge Representation,” Ph.D. thesis, Radboud University of Nijmegen, April 23, 2008. [10] John F. Sowa, 1995. “Top-level Ontological Categories,” International Journal of Human-computer Studies 43, no. 5 (1995): 669-685. [11] Attributes, Relations and Annotations comprise OWL properties. In general, Attributes correspond to the OWL datatypes property; Relations to the OWL object property; and Annotations to the OWL annotation property. These specific OWL terms are not used in our speculative grammar, however, because some attributes may be drawn from controlled vocabularies, such as colors or shapes, that can be represented as one of a list of attribute choices. In these cases, such attributes are defined as object properties. Nonetheless, the mappings of our speculative grammar to existing OWL properties is quite close. [12] As I earlier wrote, “Description logics and their semantics traditionally split concepts and their relationships from the different treatment of instances and their attributes and roles, expressed as fact assertions. The concept split is known as the TBox (for terminological knowledge, the basis for T in TBox) and represents the schema or taxonomy of the domain at hand. The TBox is the structural and intensional component of conceptual relationships. The second split of instances is known as the ABox (for assertions, the basis for A in ABox) and describes the attributes of instances (and individuals), the roles between instances, and other assertions about instances regarding their class membership with the TBox concepts.” In the diagram above, the middle column represents particulars, or the ABox components. The definition of items and the first and third columns represent TBox components.

A Fond, But Overdue, Farewell

AI3:::Adaptive Information (Mike Bergman) - Mon, 06/13/2016 - 13:28
Unveiling a New ‘Timeline of Information History’

Since I first posted it eight years ago, one of the popular features of my blog has been its Timeline of Information History. However, I’m embarrassed to say that the interactive JavaScript application has been broken now for some months. I had fixed the JS once before about four years ago, but some recent change to WordPress (or one of my plugins) again caused a JavaScript conflict of some nature. After a couple of my own attempts to fix it, I called in the cavalry, Fred Giasson, to provide more professional attention. I’m sure the application was eventually fixable, but tracking down fixes to undocumented code is ultimately a fool’s game (or for those with too much time on their hands), so it wasn’t worth further investment to understand the older Timeline JS code, including dependencies on outdated libraries. So, these past few months, the Timeline remained broken.

Until today. I found another timeline on the Web, Timeline JS3, that offers a hosted version driven by a Google spreadsheet. It operates differently and has a different look-and-feel, but it captures all of the original source information of the earlier Timeline and has a charm all its own:

I encourage you to investigate this new Timeline of Information History.

Installation Overview

TimelineJS (or JS3 in its latest version) is an open source and cloud-hosted timeline from the Knight Lab at Northwestern University. They provide a plugin to WordPress, with calls via either shortcodes or a simple PHP statement. They provide a dead-simple online form for generating your own timeline quickly, which they then host. If you prefer to fiddle with all of the dials and knobs, Knight Labs also offers code and clear instructions for calling and using the libraries locally. Their lead is “Easy-to-make, beautiful timelines,” and I agree.

In my own configuration of WordPress my Timeline of Information History is not a post, but a separate page with its own PHP template. None of the direct WordPress options suggested by Knight Labs worked for me, including the plugin, but I was able to post the code generated by the online form directly into my current PHP template. (My guess is that simple WordPress blog sites and posts would work with their standard set-up.) If there are additional style changes I want to make down the road, I will need to bring in the Timeline JS3 libraries and host them locally (there is a small suite of canned, online options; further CSS or style changes require that you have your own local install.) For now, I am deferring this possible step.

With a bit of fiddling, it was not too difficult to convert the existing XML format of my prior Timeline to the CSV (Google spreadsheet with fixed columns) format of Timeline JS3 (which actually uses the JSON generated from the spreadsheet). I also did some editing and link corrections while doing the migration. It had been a while since I had used the Google online spreadsheet. I found it much smoother and responsive than my last uses of it. Copying-and-pasting across environments also works nicely.

The <iframe> code generated by the online form worked as is when embedded in my existing PHP template. The instructions should you want to install the libraries and host locally appeared equally clear. In all, my experience installing the new Timeline and migrating its data was pleasingly smooth. But, no matter what, code, environment and data changes do take some effort. Now that it is done, I am happy with the results.

The End of My Simile Era

This marks the end of nearly a decade of use on my blog of the Simile tools from David Karger‘s shop at MIT. Two of this blog’s former tools, Exhibit and Timeline, were developed by the skilled and innovative David Huynh. David was a toolmaking fool during his MIT tenure, including Sifter and Solvent and Potluck, besides Exhibit and Timeline. After he went to Metaweb (and then Google) he developed the data wrangling tool Gridworks, which was renamed Google Refine and then Open Refine when it went open source. Any one of these tools is a notable contribution; the innovations across the whole body of Huynh’s work are quite remarkable.

I was the first to install Exhibit on WordPress outside of MIT in 2007. I installed Timeline for the Timeline of Information History in 2008. I upgraded both as libraries were updated and WP changed; especially difficult was WP’s incorporation of more JavaScript, causing JS conflicts. Though I had to retire Exhibit for these reasons in 2011, I was able to keep Timeline going until just recently. With today’s retirement of Timeline, the era of my blog’s working with Simile tools comes to an end.

I’d like to thank the Davids, Larry and others at the Simile program that made so many contributions at a pivotal time in the semantic Web and Web of data. Good job, all! We won’t soon see that era again.

WordPress is Likely Next on the Chopping Block

I have been a WordPress user, self-hosted, since Day One of this blog. My first big blog effort was a comprehensive guide to blogging with WP [1]. I’ve spent many years with WP, but it is distinctly feeling long in the tooth.

These JS conflicts that appear out of nowhere are, unfortunately, not an uncommon occurrence with WordPress. I routinely have spam, bot, and hacker attacks, probing virtually every area of my blog and trying to break into my administrative area of WP. My counters for fending off malicious probes and attacks are in the millions.

For years, my site sometimes has race conditions that I have been unable to track down and correct. There are certainly conflicts between plugins, but the relative rarity and what exactly the conditions are to trigger the race conditions have yet to be discovered. Periodically trying to track down the root issue has been frustrating. Truthfully, I still do not know what they are.

Web and UI design for the Web has evolved substantially, especially over the past years of growth and then dominance of mobile. In the case of this blog, AI3, which is solely authored and managed by me, I also do not need many of the aspects of a full-throated blog or publishing site.

WordPress also has poor performance and difficulties optimizing performance. Tuning Web servers is a nightmare for the amateur. I have tried various caching and CDN strategies. While performance can be improved with these strategies, they come at a cost of their own glitches and added complexity.

These factors have caused me to look closely at static site generators. In my style of blogging, I make many edits while drafting and may have multiple drafts being worked on over weeks. But, once published, there are not many edits. From the standpoint of the Web, reading can be emphasized over writing.

Yet, despite its simplicity and better performance, there are also challenges in workflow and tooling in going to a static site design. There is also the daunting question of how best to convert my existing WP data to an accurate, readable form without massive manual changes. I would not make the change to a different blogging platform without carrying my prior writings forward. Looked at in this way, my WordPress continues to work with the occasional burst of effort, like this current one in switching out timelines. I’m still mulling the more fundamental change away from WP. The chicken is clucking the closer I get to the chopping block.

[1] An archival version of this document, Comprehensive Guide to a Professional Blog Site: A WordPress Example, can be downloaded in PDF. But realize this guide is now more than 11 years old, and not much is likely applicable to the current Web.

Rationales for Typology Designs in Knowledge Bases

AI3:::Adaptive Information (Mike Bergman) - Mon, 06/06/2016 - 15:41

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Design is Aimed to Improve Computability

In the lead up to our most recent release of UMBEL, I began to describe our increasing reliance on the use of typologies. In this article, I’d like to expand on our reasons for this design and the benefits we see.

‘Typology’ is not a common term within semantic technologies, though it is used extensively in such fields as archaeology, urban planning, theology, linguistics, sociology, statistics, psychology, anthropology and others. In the base semantic technology language of RDF, a ‘type’ is what is used to declare an instance of a given class. This is in keeping with our usage, where an instance is a member of a type.

Strictly speaking, ‘typology’ is the study of types. However, as used within the fields noted, a ‘typology’ is the result of the classification of things according to their characteristics. As stated by Merriam Webster, a ‘typology’ is “a system used for putting things into groups according to how they are similar.” Though some have attempted to make learned distinctions between typologies and similar notions such as classifications or taxonomies [1], we think this idea of grouping by similarity is the best way to think of a typology.

In Structured Dynamics‘ usage as applied to UMBEL and elsewhere, we are less interested in the sense of ‘typology’ as comparisons across types and more interested in the classification of types that are closely related, what we have termed ‘SuperTypes’. In this classification, each of our SuperTypes gets its own typology. The idea of a SuperType, in fact, is exactly equivalent to a typology, wherein the multiple entity types with similar essences and characteristics are related to one another via a natural classification. I speak elsewhere how we actually go about making these distinctions of natural kinds [2].

In this article, I want to stand back from how a typology is constructed to deal more about their use and benefits. Below I discuss the evolution of our typology design, the benefits that accrue from the ‘typology’ approach, and then conclude with some of the application areas to which this design is most useful. All of this discussion is in the context of our broader efforts in KBAI, or knowledge-based artificial intelligence.

Evolution of the Design

I wish we could claim superior intelligence or foresight in how our typology design came about, but it was truthfully an evolution of needing to deal with pragmatic concerns in our use of UMBEL over the past near-decade. The typology design has arisen from the intersection of: 1) our efforts with SuperTypes, and creating a computable structure that uses powerful disjoint assertions; 2) an appreciation of the importance of entity types as a focus of knowledge base terminology; and 3) our efforts to segregate entities from other key constructs of knowledge bases, including attributes, relations and annotations. Though these insights may have resulted from serendipity and practical use, they have brought a new understanding of how best to organize knowledge bases for artificial intelligence uses.

The Initial Segreation into SuperTypes

We first introduced SuperTypes into UMBEL in 2009 [3]. The initiative arose because we observed about 90% of the concepts in UMBEL were disjoint from one another. Disjoint assertions are computationally efficient and help better organize a knowledge graph. To maximize these benefits we did both top-down and bottom-up testing to derive our first groupings of SuperTypes into 29 mostly disjoint types, with four non-disjoint (or cross-cutting and shared) groups [3]. Besides computational efficiency and its potential for logical operations, we also observed that these SuperTypes could also aid our ability to drive display widgets (such as being able to display geolocational types on maps).

All entity classes within a given SuperType are thus organized under the SuperType (ST) itself as the root. The classes within that ST are then organized hierarchically, with children classes having a subClassOf relation to their parent. By the time of UMBEL’s last release [4], this configuration had evolved into the following 31 largely disjoint SuperTypes, organized into 10 or so clusters or “dimensions”:

Constituents Natural Phenomena Area or Region Location or Place Shapes Forms Situations Time-related Activities Events Times Natural Matter Atoms and Elements Natural Substances Chemistry Organic Matter Organic Chemistry Biochemical Processes Living Things Prokaryotes Protists & Fungus Plants Animals Diseases Agents Persons Organizations Geopolitical Artifacts Products Food or Drink Drugs Facilities Information Audio Info Visual Info Written Info Structured Info Social Finance & Economy Society Current SuperType Structure of UMBEL

We also used the basis in SuperTypes to begin cleaving UMBEL into modules, with geolocational types being the first to be separated. We initially began splitting into modules as a way to handle UMBEL’s comparatively large size (~ 30K concepts). As we did so, however, we also observed that most of the SuperTypes could be also be segregated into modules. This architectural view and its implications were another reason leading to the eventual typology design.

A Broadening Appreciation for the Pervasiveness of Entity Types

The SuperType tagging and possible segregation of STs into individual modules led us to review other segregations and tags. Given that the SuperTypes were all geared to entities and entity types — and further represented about 90% of all concepts in UMBEL — we began to look at entities as a category with more care and attention. This analysis took us back to the beginnings of entity recognition and tagging in natural language processing. We saw the progression of understanding from named entities and just a few entity types, to the more recent efforts in so-called fine-grained entity recognition [5].

What was blatantly obvious, but which had been previously overlooked by us and other researchers investigating entity types, was that most knowledge graphs (or upper ontologies) were themselves made of largely entity types [5]. In retrospect, this should not be surprising. Most knowledge graphs deal with real things in the world, which, by definition, tend to be entities. Entities are the observable, often nameable, things in the world around us. And how we organize and refer to those entities — that is, the entity types — constitutes the bulk of the vocabulary for a knowledge graph.

We can see this progression of understanding moving from named entities and fine-grained entity types, all the way through to an entity typology — UMBEL’s SuperTypes — that then becomes the tie-in point for individual entities (the ABox):


Evolving Sophistication of Entity Types

The key transition is moving from the idea of discrete numbers of entity types to a system and design that supports continuous interoperability through an “accordion-like” typology structure.

The General Applicability of ‘Typing’ to All Aspects of Knowledge Bases

The “type-orientation” of a typology was also attractive because it offers a construct that can be applied to all other (non-entity) parts of the knowledge base. Actions can be typed; attributes can be typed; events can be typed; and relations can be typed. A mindset around natural kinds and types helps define the speculative grammar of KBAI (a topic of a next article). We can thus represent these overall structural components in a knowledge base as:

Typology View of a Knowledge Base

The shading is in reference to that which is external to the scope of UMBEL.

The intersection of these three factors — SuperTypes, an “accordion” design for continuous entity types, and overall typing of the knowledge base — set the basis for how to formalize an overall typology design.

Formalizing the Typology Design

We have first applied this basis to typologies for entities, based on the SuperTypes. Each SuperType becomes its own typology with natural boundaries and a hierarchical structure. No instances are allowed in the typology; only types.

Initial construction of the typology first gathers the relevant types (concepts) and automatically evaluates those concepts for orphans (unconnected concepts) and fragments (connected portions missing intermediary parental concepts). For the initial analysis, there are likely multiple roots, multiple fragments, and multiple orphans. We want to get to a point where there is a single root and all concepts in the typology are connected. Source knowledge bases are queried for the missing concepts and evaluated again in a recursive manner. Candidate placements are then written to CSV files and evaluated with various utilities, including crucially manual inspection and vetting. (Because the system bootstraps what is already known and structured in the system, it is important to build the structure with coherent concepts and relations.)

Once the overall candidate structure is completed, it is then analyzed against prior assignments in the knowledge base. ST disjoint analysis, coherent inferencing, and logical placement tests again prompt the creation of CSV files that may be viewed and evaluated with various utilities, but, again, ultimately manually vetted.

The objective of the build process is a fully connected typology that passes all coherency, consistency, completeness and logic tests. If errors are subsequently discovered, the build process must be run again with possible updates to the processing scripts. Upon acceptance, each new type added to a typology should pass a completeness threshold, including a definition, synonyms, guideline annotations, and connections. The completed typology may be written out in both RDF and CSV formats. (The current UMBEL and its typologies are available here.)

Integral to the design must be build, testing and maintenance routines, scripts, and documentation. Knowledge bases are inherently open world [6], which means that the entities and their relationships and characteristics are constantly growing and changing due to new knowledge underlying the domain at hand. Such continuous processing and keeping track of the tests, learnings and workflow steps place a real premium on literate programming, about which Fred Giasson, SD’s CTO, is now writing [7].

Because of the very focused nature of each typology (as set by its root), each typology can be easily incorporated or excised from a broader structure. Each typology is rather simple in scope and simple in structure, given its hierarchical nature. Each typology is readily maintained and built and tested. Typologies pose relatively small ontological commitments.

Benefits of the Design

The simple bounding and structure of the typology design makes each typology understandable merely by inspecting its structure. But the typologies can also be read into programs such as Protégé in order to inspect or check complete specifications and relationships.

Because each typology is (designed to be) coherent and consistent, new concepts or structures may be related to any part of its hierarchical design. This gives these typologies an “accordion-like” design, similar to the multiple levels and aggregation made possible by an accordion menu:

An ‘Accordion’ Design Accommodates Different Granularities

The combination of logical coherence with a flexible, accordion structure gives typologies a unique set of design benefits. Some have been mentioned before, but to recap they are:

Computable

Each type has a basis — ranging from attributes and characteristics to hierarchical placement and relationship to other types — that can inform computability and logic tests, potentially including neighbor concepts. Ensuring that type placements are accurate and meet these tests means that the now-placed types and their attributes may be used to test the placement and logic of subsequent candidates. The candidates need not be only internal typology types, but may also be used against external sources for classification, tagging or mapping.

Because the essential attributes or characteristics across typologies in an entire domain can differ broadly — such as entities v attributes, living v inanimate things, natural things v man-made things, ideas v physical objects, etc. — it is possible to make disjointedness assertions between entire groupings of natural classes. Disjoint assertions, combined with logical organization and inference, provide a typology design that lends itself to reasoning and tractability.

The internal process to create these typologies also has the beneficial effect of testing placements in the knowledge graph and identifying gaps in the structure as informed by fragments and orphans. This computability of the structure is its foundational benefit, since it determines the accuracy of the typology itself and drives all other uses and services.

Pluggable and Modular

Since each typology has a single root, it is readily plugged into or removed from the broader structure. This means the scale and scope of the overall system may be easily adjusted, and the existing structure may be used as a source for extensions (see next). Unlike more interconnected knowledge graphs (which can have many network linkages), typologies are organized strictly along these lines of shared attributes, which is both simpler and also provides an orthogonal means for investigating type-class membership.

Interoperable

The idea of nested, hierarchical types organized into broad branches of different typologies also provides a very flexible design for interoperating with a diversity of world views and degrees of specificity. A typology design, logically organized and placed into a consistent grounding of attributes, can readily interoperate with these different world views. So far, with UMBEL, this interoperable basis is limited to concepts and things, since only the entity typologies have been initially completed. But, once done, the typologies for attributes and relations will extend this basis to include full data interoperability of attribute:value pairs.

Extensible

A typology design for organizing entities can thus be visualized as a kind of accordion or squeezebox, expandable when detail requires, or collapsed to more coarse-grained when relating to broader views. The organization of entity types also has a different structure than the more graph-like organization of higher-level conceptual schema, or knowledge graphs. In the cases of broad knowledge bases, such as UMBEL or Wikipedia, where 70 percent or more of the overall schema is related to entity types, more attention can now be devoted to aspects of concepts or relations.

Each class within the typology can become a tie-in point for external information, providing a collapsible or expandable scaffolding (the ‘accordion’ design). Via inferencing, multiple external sources may be related to the same typology, even though at different levels of specificity. Further, very detailed class structures can also be accommodated in this design for domain-specific purposes. Moreover, because of the single tie-in point for each typology at its root, it is also possible to swap out entire typology structures at once, should design needs require this flexibility.

Testable and Maintainable

The only sane way to tackle knowledge bases at these structural levels is to seek consistent design patterns that are easier to test, maintain and update. Open world systems must embrace repeatable and largely automated workflow processes, plus a commitment to timely updates, to deal with the constant, underlying change in knowledge.

Listing of Broad Application Areas

Some of the more evident application areas for this design — and in keeping with current client and development activities for Structured Dynamics — are the following:

  • Domain extension — the existing typologies and their structure provide a ready basis for adding domain details and extensions;
  • Tagging — there are many varieties of tagging approaches that may be driven from these structures, including, with the logical relationships and inferencing, ontology-based information tagging;
  • Classification — the richness of the typology structures means that any type across all typologies may be a possible classification assignment when evaluating external content, if the overall system embracing the typologies is itself coherent;
  • Interoperating datasets — the design is based on interoperating concepts and datasets, and provides more semantic and inferential means for establishing MDM systems;
  • Machine learning (ML) training — the real driver behind this design is lowering the costs for supervised machine learning via more automated and cost-effective means of establishing positive and negative training sets. Further, the system’s feature richness (see next) lends itself to unsupervised ML techniques as well; and
  • Rich feature set — a design geared from the get-go to emphasize and expose meaningful knowledge base features [8] perhaps opens up many new fruitful avenues for machine learning and other AI. More expressed structure may help in the interpretability of latent feature layers in deep learning. In any case, more and coherent structure with testability can only be goodness for KBAI going forward.
One Building Block Among Many

The progressions and learning from the above were motivated by the benefits that could be seen with each structural change. Over nearly a decade, as we tried new things, structured more things, we discovered more things and adapted our UMBEL design accordingly. The benefits we see from this learning are not just additive to benefits that might be obtained by other means, but they are systemic. The ability to make knowledge bases computable — while simultaneously increasing the features space for training machine learners — at much lower cost should be a keystone enabler at this particular point in AI’s development. Lowering the costs of creating vetted training sets is one way to improve this process. 

Systems that can improve systems always have more leverage than individual innovations. The typology design outlined above is the result of the classification of things according to their shared attributes and essences. The idea is that the world is divided into real, discontinuous and immutable ‘kinds’. Expressed another way, in statistics, typology is a composite measure that involves the classification of observations in terms of their attributes on multiple variables. In the context of a global KB such as Wikipedia, about 25,000 entity types are sufficient to provide a home for the millions of individual articles in the system.

As our next article will discuss, Charles Sanders Peirce’s consistent belief that the real world can be logically conceived and organized provides guidance for how we can continue to structure our knowledge bases into computable form. We now have a coherent base for treating types and natural classes as an essential component to that thinking. These insights are but one part of the KB innovations suggested by Peirce’s work.

[1] See, for example, Alberto Marradi, 1990. “Classification, Typology, Taxonomy“, Quality & Quantity 24, no. 2 (1990): 129-157. [2] M.K. Bergman, 2015. “‘Natural Classes’ in the Knowledge Web,” AI3:::Adaptive Information blog, July 13, 2015. [3] M.K. Bergman, 2009. “‘SuperTypes’ and Logical Segmentation of Instances,” AI3:::Adaptive Information blog, September 2, 2009. [4] umbel.org, “New, Major Upgrade of UMBEL Released,” UMBEL press release, May 10, 2016 (for UMBEL v. 1.50 release) [5] M.K. Bergman, 2016. “How Fine Grained Can Entity Types Get?,” AI3:::Adaptive Information blog, March 8, 2016. [6] M.K. Bergman, 2012. “The Open World Assumption: Elephant in the Room,” AI3:::Adaptive Information blog, December 21, 2009. [7] See http://fgiasson.com/blog/index.php/category/programming/literate-programming/; the last update was, Frédérick Giasson, 2016. “Creating and Running Unit Tests Directly in Source Files with Org-mode“, fgiasson.com/blog, May 30, 2016. [8] M.K. Bergman, 2015. “A (Partial) Taxonomy of Machine Learning Features,” AI3:::Adaptive Information blog, November 23, 2015.

Squatty Potty and Millenials

AI3:::Adaptive Information (Mike Bergman) - Wed, 06/01/2016 - 07:03
Checking Out Where Things Sit from Upwind

I have distinct memories of drinking booze and swimming in the faculty pool, chasing out the National Guard, and facing Capt. Joel Honey in downtown Santa Barbara. UCSB and Isla Vista, over multiple occasions, were but one of many focal points for anti-war demonstrations during Vietnam. There was actually more than one summer of love, and it was hard to cut my hair. (It was even harder to grow a beard.) I even lived in a treehouse for a summer. My generation was politically active, engaged, high, and mostly free from STDs. Peace, love, dope.

We were empowered with new political and social consciences and better ideas and ideals than our parents. The whole materialistic thing was a drag. We were hip, we fed our heads, and we burned our tighty whiteys (or bras, depending). It seems so innocent now that we could actually stick out our thumbs and hitchhike across the country. Everything was actually pretty cool, except for crabs.

Then, this past Christmas, my kids and their partners (used to be what we called significant others), introduced my wife (partner) and me to a new perspective: Squatty Potty. We howled like hyenas watching the video, but it was only a laugh at that time.

Now, my kids (with their partners), all heading to get their medical degrees, and so should know something about bodily stuff, have raised again the better angle-of-attack of Squatty Potty. They are faithful adherents (or exherents, depending on your perspective). Only now the sentiment is not laughs; it is reverence. It turns out that my generation, and our parental generation of squares, and perhaps for generations, have not really known how to shit. We may have been wasting TP, too (but that is largely unspoken).

It was this second reference to Squatty Potty that caused me in repose to wonder: What was it with these millenials? Why aren’t they hip like we used to be? Why do I feel so constipated?

See, these millenials are constantly talking about local organic food, clean air, keeping the planet in balance, a clean colon. In just a generation, we have advanced from politics to emissions, global and personal. I actually think this is progress. We have embraced the global, but turned it inward. We can monitor our progress to a polyp-free alimentary canal!

So, there is a reason that Millenials have a smug look when you see them on the street. They know how to breathe, eat and shit like no generation before them. We have progressed as a society from one of ideas and political protest, to how to feed and void ourselves. Still, I think getting at the basics is a good idea. This generation coming down the chute knows what it takes to keep a clear pathway ahead.

New, Major Upgrade of UMBEL Released

AI3:::Adaptive Information (Mike Bergman) - Wed, 05/11/2016 - 13:55
Version 1.50 Fully Embraces a Typology Design, Gets Other Computability Improvements

The year since the last major release of UMBEL (Upper Mapping and Binding Exchange Layer) has been spent in a significant re-think of how the system is organized. Four years ago, in version 1.05, we began to split UMBEL into a core and a series of swappable modules. The first module adopted was in geographical information; the second was in attributes. This design served us well, but it was becoming apparent that we were on a path of multiple modules. Each of UMBEL’s major so-called ‘SuperTypes‘ — that is, major cleavages of the overall UMBEL structure that are largely disjoint from one another, such as between Animals and Facilities — were amenable to the module design. This across-the-board potential cleavage of the UMBEL system caused us to stand back and question whether a module design alone was the best approach. Ultimately, after much thought and testing, we adopted instead a typology design that brought additional benefits beyond simple modularity.

Today, we are pleased to announce the release of these efforts in UMBEL version 1.50. Besides standard release notes, this article discusses this new typology design, and explains its uses and benefits.

Basic UMBEL Background

The Web and enterprises in general are characterized by growing, diverse and distributed information sources and data. Some of this information resides in structured databases; some resides in schema, standards, metadata, specifications and semi-structured sources; and some resides in general text or media where the content meaning is buried in unstructured form. Given these huge amounts of information, how can one bring together what subsets are relevant? And, then for candidate material that does appear relevant, how can it be usefully combined or related given its diversity? In short, how does one go about actually combining diverse information to make it interoperable and coherent?

UMBEL thus has two broad purposes. UMBEL’s first purpose is to provide a general vocabulary of classes and predicates for describing and mapping domain ontologies, with the specific aim of promoting interoperability with external datasets and domains. UMBEL’s second purpose is to provide a coherent framework of reference subjects and topics for grounding relevant Web-accessible content. UMBEL presently has about 34,000 of these reference concepts drawn from the Cyc knowledge base, organized into 31 mostly disjoint SuperTypes.

The grounding of information mapped by UMBEL occurs by common reference to the permanent URIs (identifiers) for UMBEL’s concepts. The connections within the UMBEL upper ontology enable concepts from sources at different levels of abstraction or specificity to be logically related. Since UMBEL is an open source extract of the OpenCyc knowledge base, it can also take advantage of the reasoning capabilities within Cyc.

Diagram showing linked data datasets. UMBEL is near the hub, below and to the right of the central DBpedia.

UMBEL’s vocabulary is designed to recognize that different sources of information have different contexts and different structures, and meaningful connections between sources are not always exact. UMBEL’s 34,000 reference concepts form a knowledge graph of subject nodes that may be related to external classes and individuals (instances and entities). Via this coherent structure, we gain some important benefits:

  • Mapping to other ontologies — disparate and heterogeneous datasets and ontologies may be related to one another by mapping to the UMBEL structure
  • A scaffolding for domain ontologies — more specific domain ontologies can be made interoperable by using the UMBEL vocabulary and tieing their more general concepts into the UMBEL structure
  • Inferencing — the UMBEL reference concept structure is coherent and designed for inferencing, which supports better semantic search and look-ups
  • Semantic tagging — UMBEL, and ontologies mapped to it, can be used as input bases to ontology-based information extraction (OBIE) for tagging text or documents; UMBEL’s “semsets” broaden these matches and can be used across languages
  • Linked data mining — via the reference ontology, direct and related concepts may be retrieved and mined and then related to one another
  • Creating computable knowledge bases — with complete mappings to key portions of a knowledge base, say, for Wikipedia articles, it is possible to use the UMBEL graph structure to create a computable knowledge source, with follow-on benefits in artificial intelligence and KB testing and improvements, and
  • Categorizing instances and named entities — UMBEL can bring a consistent framework for typing entities and relating their descriptive attributes to one another.

UMBEL is written in the semantic Web languages of SKOS and OWL 2. It is a class structure used in linked data, along with other reference ontologies. Besides data integration, UMBEL has been used to aid concept search, concept definitions, query ranking, ontology integration, and ontology consistency checking. It has also been used to build large ontologies and for online question answering systems [1].

Including OpenCyc, UMBEL has about 65,000 formal mappings to DBpedia, PROTON, GeoNames, and schema.org, and provides linkages to more than 2 million Wikipedia pages (English version). All of its reference concepts and mappings are organized under a hierarchy of 31 different SuperTypes, which are mostly disjoint from one another. Development of UMBEL began in 2007. UMBEL was first released in July 2008. Version 1.00 was released in February 2011.

Summary of Version 1.50 Changes

These are the principal changes between the last public release, version 1.20, and this version 1.50. In summary, these changes include:

  • Removed all instance or individual listings from UMBEL; this change does NOT affect the punning used in UMBEL’s design (see Metamodeling in Domain Ontologies)
  • Re-aligned the SuperTypes to better support computability of the UMBEL graph and its resulting disjointedness
  • These SuperTypes were eliminated with concepts re-assigned: Earthscape, Extraterrestrial, Notations and Numbers
  • These new SuperTypes were introduced: AreaRegion, AtomsElements, BiologicalProcesses, Forms, LocationPlaces, and OrganicChemistry, with logically reasoned assignments of RefConcepts
  • The Shapes SuperType is a new ST that is inherently non-disjoint because it is shared with about half of the RefConcepts
  • The Situations is an important ST, overlooked in prior efforts, that helps better establish context for Activities and Events
  • Made re-alignments in UMBEL’s upper structure and introduced additional upper-level categories to better accommodate these refinements in SuperTypes
  • A typology was created for each of the resulting 31 disjoint STs, which enabled missing concepts to be identified and added and to better organize the concepts within each given ST
  • The broad adoption of the typology design for all of the (disjoint) SuperTypes also meant that prior module efforts, specifically Geo and Attributes, could now be made general to all of UMBEL. This re-integration also enabled us to retire these older modules without affecting functionality
  • The tests and refinements necessary to derive this design caused us to create flexible build and testing scripts, documented via literate programming (using Clojure)
  • Updated all mappings to DBpedia, Wikipedia, and schema.org
  • Incorporated donated mappings to five additional LOV vocabularies [2]
  • Tested the UMBEL structure for consistency and coherence
  • Updated all prior UMBEL documentation
  • Expanded and updated the UMBEL.org Web site, with access and demos of UMBEL.
UMBEL’s SuperTypes

The re-organizations noted above have resulted in some minor changes to the SuperTypes and how they are organized. These changes have made UMBEL more computable with a higher degree of disjointedness between SuperTypes. (Note, there are also organizational SuperTypes that work largely to aid the top levels of the knowledge graph, but are explicitly designed to NOT be disjoint. Important SuperTypes in this category include Abstractions, Attributes, Topics, Concepts, etc. These SuperTypes are not listed below.)

UMBEL thus now has 31 largely disjoint SuperTypes, organized into 10 or so clusters or “dimensions”:

Constituents Natural Phenomena Area or Region Location or Place Shapes Forms Situations Time-related Activities Events Times Natural Matter Atoms and Elements Natural Substances Chemistry Organic Matter Organic Chemistry Biochemical Processes Living Things Prokaryotes Protists & Fungus Plants Animals Diseases Agents Persons Organizations Geopolitical Artifacts Products Food or Drink Drugs Facilities Information Audio Info Visual Info Written Info Structured Info Social Finance & Economy Society

These disjoint SuperTypes provide the basis for the typology design described next.

The Typology Design

After a few years of working with SuperTypes it became apparent each SuperType could become its own “module”, with its own boundaries and hierarchical structure. Since across the UMBEL structure nearly 90% of the reference concepts are themselves entity classes, if these are properly organized, we can achieve a maximum of disjointness, modularity, and reasoning efficiency. Our early experience with modules pointed the way to a design for each SuperType that was as distinct and disjoint from other STs as possible. And, through a logical design of natural classes [3] for the entities in that ST, we could achieve a flexible, ‘accordion-like’ design that provides entity tie-in points from the general to the specific for each given SuperType. The design is effective for being able to interoperate across both fine-grained and coarse-grained datasets. For specific domains, the same design approach allows even finer-grained domain concepts to be effectively integrated.

All entity classes within a given SuperType are thus organized under the SuperType itself as the root. The classes within that ST are then organized hierarchically, with children classes having a subClassOf relation to their parent. Each class within the typology can become a tie-in point for external information, providing a collapsible or expandable scaffolding (the ‘accordion’ design). Via inferencing, multiple external sources may be related to the same typology, even though at different levels of specificity. Further, very detailed class structures can also be accommodated in this design for domain-specific purposes. Moreover, because of the single tie-in point for each typology at its root, it is also possible to swap out entire typology structures at once, should design needs require this flexibility.

We have thus generalized the earlier module design to where every (mostly) disjoint SuperType now has its own separate typology structure. The typologies provide the flexible lattice for tieing external content together at various levels of specificity. Further, the STs and their typologies may be removed or swapped out at will to deal with specific domain needs. The design also dovetails nicely with UMBEL’s build and testing scripts. Indeed, the evolution of these scripts via literate programming has also been a reinforcing driver for being able to test and refine the complete ST and typologies structure.

Still a Work in Progress

Though UMBEL retains its same mission as when the system was first formulated nearly a decade ago, we also see its role expanding. The two key areas of expansion are in UMBEL’s use to model and map instance data attributes and in acting as a computable overlay for Wikipedia (and other knowledge bases). These two areas of expansion are still a work in progress.

The mapping to Wikipedia is now about 85% complete. While we are testing automated mapping mechanisms, because of its central role we also need to vet all UMBEL-Wikipedia mapping assignments. This effort is pointing out areas of UMBEL that are over-specified, under-specified, and sometimes duplicative or in error. Our goal is to get to a 100% coverage point with Wikipedia, and then to exercise the structure for machine learning and other tests against the KB. These efforts will enable us to enhance the semsets in UMBEL as well as to move toward multilingual versions. This effort, too, is still a work in progress.

Despite these desired enhancements, we are using all aspects of UMBEL and its mappings to both aid these expansions and to test the existing mappings and structure. These efforts are proving the virtuous circle of improvements that is at the heart of UMBEL’s purposes.

Where to Get UMBEL and Learn More

The UMBEL Web site provides various online tools and Web services for exploring and using UMBEL. The UMBEL GitHub site is where you can download the UMBEL Vocabulary or the UMBEL Reference Concept ontology, both under a Creative Commons Attribution 3.0 license. Other documents and backup are also available from that location.

Technical specifications for UMBEL and its various annexes are available from the UMBEL wiki site. You can also download a PDF version of the specifications from there. You are also welcomed to participate on the UMBEL mailing list or LinkedIn group.

[1] See further https://en.wikipedia.org/wiki/UMBEL. [2] Courtesy of Jana Vataščinová (University of Economics, Prague) and Ondřej Zamazal (University of Economics, Prague, COSOL project). [3] See, for example, M.K. Bergman, 2015. “‘Natural Classes’ in the Knowledge Web,” AI3:::Adaptive Information blog, July 13, 2015.

‘Deep Graphs’: A New Framework for Network Analysis

AI3:::Adaptive Information (Mike Bergman) - Tue, 04/05/2016 - 21:28
New Method Appears Promising for Machine Learning, Feature Generation

An exciting new network analysis framework was published today. The paper, Deep Graphs – A General Framework to Represent and Analyze Heterogeneous Complex Systems Across Scales, presents the background information and derivation of methods applied to this new approach for analyzing networks [1]. The authors of the paper, Dominik Traxl, Niklas Boers and Jürgen Kurths, also released the open source DeepGraph network analysis package, written in Python, for undertaking and conducting the analysis. Detailed online documentation accompanies the entire package.

The basic idea behind Deep Graphs is to segregate graph nodes and edges into types, which form supernodes and superedges, respectively. These grouped types then allow the graph to be partitioned into lattices, which can be intersected (combinations of nodes and edges) into representing deeper graph structures embedded in the initial graph. The method can be applied to a graph representation of anything, since the approach is grounded in the graph primitives of nodes and edges using a multi-layer network (MLN) representation.

These deeper graph structures can themselves be used as new features for machine learning or other applications. A deep graph, which the authors formally define as a geometric partition lattice of the source graph, conserves the original information in the graph and allows it to be redistributed to the supernodes and superedges. Intersections of these may surface potentially interesting partitions of the graph that deserve their own analysis.

The examples the authors present show the suitability of the method for time-series data, using precipitation patterns in South America. However, as noted, the method applies to virtually any data that can be representated as a graph.

Though weighted graphs and other techniques have been used, in part, for portions of this kind of analysis in the past, this appears to be the first generalized method applicable to the broadest ways to aggregate and represent graph information. The properties associated with a given node may similarly be representated and aggregated. The aggregation of attributes may provide an additional means for mapping and relating external datasets to one another.

There are many aspects of this approach that intrigue us here at Structured Dynamics. First, we are always interested in network and graph analytical techniques, since all of our source schema are represented as knowledge graphs. Second, our specific approach to knowledge-based artificial intelligence places a strong emphasis on types and typologies for organizing entities (nodes and event relations) and we also separately segregate attribute property information [2]. And, last, finding embedded superstructures within the source graphs should also work to enhance the feature sets available for supervised machine learning.

We will later post our experiences in working with this promising framework.

[1] Dominik Traxl, Niklas Boers and Jürgen Kurths, “Deep Graphs – A General Framework to Represent and Analyze Heterogeneous Complex Systems Across Scales“, arXiv:1604.00971, April 5, 2016. To be published in Chaos: An Interdisciplinary Journal of Nonlinear Science. [2] See M. K. Bergman, 2014. “Knowledge-based Artificial Intelligence,” from AI3:::Adaptive Information blog, November 17, 2014.

Withstanding the Test of Time

AI3:::Adaptive Information (Mike Bergman) - Mon, 03/28/2016 - 16:50
Long-lost Global Warming Paper is Still Pretty Good

My first professional job was being assistant director and then project director for a fifty-year look at the future of coal use by the US Environmental Protection Agency. The effort, called the Coal Technology Assessment (CTA), was started under the Carter Administration in the late 1970s, and then completed after Reagan took office in 1981. That era also spawned the Congressional Office of Technology Assessment. Trying to understand and forecast technological change was a big deal at that time.

 We produced many, many reports from the CTA program, some of which were never published because of politics and whether they were at odds or not with official policies of one or the other administration. Nonetheless, we did publish quite a few reports. Perhaps it is the sweetness of memory, but I also recollect we did a pretty good job. Now that more than 35 years have passed, it is possible to see whether we did a good job or not in our half-century forecasts.

The CTA program was the first to publish an official position of EPA on global warming [1], which we also backed up with a more formal academic paper [2]. I have thought much of that paper on occasion over the years, but I did not have a copy myself and only had a memory, but not hard copy, of the paper.

Last week, however, I was contacted by a post-doctoral researcher in Europe trying to track down early findings and recollections of some of the earliest efforts on global climate change. She had a copy of our early paper and was kind enough to send me a copy. I have since been able to find other copies online [2].

In reading over the paper again, I am struck by two things. First, the paper is pretty good, and still captures (IMO) the uncertainty of the science and how to conduct meaningful policy in the face of that uncertainty. And, second, but less positive, is the sense of how little truly has gotten done in the intervening decades. This same sense of déjà vu all over again applies to many of the advanced energy technologies — such as fuel cells, photovoltaics, and passive solar construction — we were touting at that time.

Of course, my own career has moved substantially from energy technologies and policy to a different one of knowledge representation and artificial intelligence. But, it is kind of cool to look back on the passions of youth, and to see that my efforts were not totally silly. It is also kind of depressing to see how little has really changed in nearly four decades.

[1] M.K. Bergman, 1980. “Atmospheric Pollution: Carbon Dioxide,” Environmental Outlook — 1980, Strategic Analysis Group, U.S. Environmental Protection Agency, EPA 600/8 80 003, July 1980, pp. 225-261. [1] Kan Chen, Richard C. Winter, and Michael K. Bergman, 1980. “Carbon dioxide from fossil fuels: Adapting to uncertainty.” Energy Policy 8, no. 4 (1980): 318-330.

A Foundational Mindset: Firstness, Secondness, Thirdness

AI3:::Adaptive Information (Mike Bergman) - Mon, 03/21/2016 - 16:26

Download as PDF

Unlocking Some Insights into Charles Sanders Peirce’s Writings

I first encountered Charles Sanders Peirce from the writings of John Sowa about a decade ago. I was transitioning my research interests from search and the deep Web to the semantic Web. Sowa’s writings are an excellent starting point for learning about logic and ontologies [1]. I was particularly taken by Sowa’s presentation on the role of signs in our understanding of language and concepts [2]. Early on it was clear to me that knowledge modeling needed to focus on the inherent meaning of things and concepts, not their surface forms and labels. Sowa helped pique my interest that Peirce’s theory of semiotics was perhaps a foundational basis for getting at these ideas.

In the decade since that first encounter, I have based my own writings on Peirce’s insights on a number of occasions [3]. I have also developed a fascination into his life and teachings and thoughts across many topics. I have become convinced that Peirce was the greatest American combination of philosopher, logician, scientist and mathematician, and quite possibly one of the greatest thinkers ever. While the current renaissance in artificial intelligence can certainly point to the seminal contributions of George Boole, Claude Shannon, and John von Neumann in computing and information theory (of course among many others), my own view, not alone, is that C.S. Peirce belongs in those ranks from the perspective of knowledge representation and the meaning of information.

“The primary task of ontology, as it was practiced by its founder Aristotle, is to bridge the gap between what exists and the languages, both natural and artificial, for talking and reasoning about what exists.” John Sowa [4]

Peirce is hard to decipher, for some of the reasons outlined below. Yet I have continued to try to crack the nut of Peirce’s insights because his focus is so clearly on the organization and categorization of information, essential to the knowledge foundations and ontologies at the center of Structured Dynamics‘ client activities and my own intellectual passions. Most recently, I had one of those epiphanies from my study of Peirce that scientists live for, causing me to change perspective from specifics and terminology to one of mindset and a way to think. I found a key to unlock the meaning basis of information, or at least one that works for me. I try to capture a sense of those realizations in this article.

A Starting Point: Peirce’s Triadic Semiosis

Since it was the idea of sign-forming and the nature of signs in Peirce’s theory of semiosis that first caught my attention, it makes sense to start there. The figure to the right shows Peirce’s understanding of the basic, triadic nature of the sign. Triangles and threes pervade virtually all aspects of Peirce’s theories and metaphysics.

For Peirce, the appearance of a sign starts with the representamen, which is the trigger for a mental image (by the interpretant) of the object [20]. The object is the referent of the representamen sign. None of the possible bilateral (or dyadic) relations of these three elements, even combined, can produce this unique triadic perspective. A sign can not be decomposed into something more primitive while retaining its meaning.

A sign is an understanding of an “object” as represented through some form of icon, index or symbol, from environmental to visual to aural or written. Complete truth is the limit where the understanding of the object by the interpretant via the sign is precise and accurate. Since this limit is rarely (ever?!) achieved, sign-making and understanding is a continuous endeavor. The overall process of testing and refining signs so as to bring understanding to a more accurate understanding is what Peirce called semiosis [5].

In Peirce’s world view — at least as I now understand it — signs are the basis for information and life (yes, you read that right) [6]. Basic signs can be building blocks for still more complex signs. This insight points to the importance of the ways these components of signs relate to one another, now adding the perspective of connections and relations and continuity to the mix.

Because the interpretant is an integral component of the sign, the understanding of the sign is subject to context and capabilities. Two different interpretants can derive different meanings from the same representation, and a given object may be represented by different tokens. When the interpretant is a human and the signs are language, shared understandings arise from the meanings given to language by the community, which can then test and add to the truth statements regarding the object and its signs, including the usefulness of those signs. Again, these are drivers to Peirce’s semiotic process.

Thinking in Threes: Context for Peirce’s Firstness, Secondness, Thirdness

As Peirce’s writings and research evolved over the years, he came to understand more fundamental aspects of this sign triad. Trichotomies and triads permeate his theories and writings in logic, realism, categories, cosmology and metaphysics. He termed this tendency and its application in the general as Firstness, Secondness and Thirdness. In Peirce’s own words [7]:

“The first is that whose being is simply in itself, not referring to anything nor lying behind anything. The second is that which is what it is by force of something to which it is second. The third is that which is what it is owing to things between which it mediates and which it brings into relation to each other.” (CP 2.356)

Peirce’s fascination with threes is not unique. In my early career designing search engines, we often used threes as quick heuristics for setting weights and tuning parameters. We note that threes are at the heart of the Resource Description Framework data model, with its subject–predicate–object ‘triples’ that are its basic statements and assertions. The logic gates of transistors are based on threes. From an historical perspective prior to Peirce, scholastic philosophers, ranging from Duns Scotus and the Modists from medieval times to John Locke and Immanuel Kant with his three formulations, expressed much of their thinking in threes [8]. As Locke wrote in 1690 [9]:

“The ideas that make up our complex ones of corporeal substances are of three sorts. First, the ideas of the primary qualities of things, which are discovered by our senses, and are in them even when we perceive them not; such are the bulk, figure, number, situation, and motion of the parts of bodies which are really in them, whether we take notice of them or no. Secondly, the sensible secondary qualities which, depending on these, are nothing but the powers these substances have to produce several ideas in us by our senses; which ideas are not in the things themselves otherwise than as anything is in its cause. Thirdly, the aptness we consider in any substance to give or receive such alteration of primary qualities, as that the substance, so altered should produce in us different ideas from what it did before.”

More recently, one the pioneers of artificial intelligence, Marv Minksy, who passed away in late January, noted his penchant for threes [10]:

Marv Minksky on
the Philosophy of Thinking in Threes

But in knowledge representation, as practiced today in foundational or upper ontologies, the organizational view of the world is mostly binary. Upper ontologies often reflect one or more of these kinds of di-chotomies [11,12] (to pick up on Minksy’s joke):

  • abstract-physical — a split between what is fictional or conceptual and what is tangibly real
  • occurrent-continuant — a split between a “snapshot” view of the world and its entities versus a “spanning” view that is explicit about changes in things over time
  • perduant-endurant — a split for how to regard the identity of individuals, either as a sequence of individuals distinguished by temporal parts (for example, childhood or adulthood) or as the individual enduring over time
  • dependent-independent — a split between accidents (which depend on some other entity) and substances (which are independent)
  • particulars-universals — a split between individuals in space and time that cannot be attributed to other entities versus abstract universals such as properties that may be assigned to anything, or
  • determinate-indeterminate.

While it is true that most of these distinctions are important ones in a foundational ontology, that does not mean that the entire ontology space should be dichotomized between them. Further, with the exception of Sowa’s ontology [4], none of the more common upper ontologies embrace any semblance of Peirce’s triadic perspective. Further, even Sowa’s ontology only partially applies Peircean principles, and it has been criticized on other grounds as well [11].

The triadic model of signs was built and argued by Peirce as the most primitive basis for applying logic suitable for the real world, with conditionals, continua and context. Truthfulness and verifiability of assertions is by nature variable. The ability of the primitive logic to further categorize the knowledge space led Peirce to elaborate well a 10-sign system, followed by a 28-sign and then a 66-sign one [13]. Neither of the two larger systems were sufficiently described by Peirce before his death. Though Peirce notes in multiple places the broad applicability of the logic of semiosis to things like crystal formation, the emergence of life, animal communications, and automation, his primary focus appears to have been human language and signs used to convey concepts and thoughts. But we are still mining Peirce’s insights, with only about 25% of his writings yet published [14].

The nature needed to be the sign because that is how information is conveyed, and the trichotomy parts were the fewest “decomposable” needed to model the real world; we would call these “primitives” in modern terminology. Here are some of Peirce’s thoughts as to what makes something “indecomposable” (in keeping with his jawbreaking terminology) [7]:

“It is a priori impossible that there should be an indecomposable element which is what it is relatively to a second, a third, and a fourth. The obvious reason is that that which combines two will by repetition combine any number. Nothing could be simpler; nothing in philosophy is more important.” (CP 1.298)

“We find then a priori that there are three categories of undecomposable elements to be expected in the phaneron: those which are simply positive totals, those which involve dependence but not combination, those which involve combination.” (CP 1.299)

“I will sketch a proof that the idea of meaning is irreducible to those of quality and reaction. It depends on two main premisses. The first is that every genuine triadic relation involves meaning, as meaning is obviously a triadic relation. The second is that a triadic relation is inexpressible by means of dyadic relations alone. . . . every triadic relation involves meaning.” (CP 1.345)

“And analysis will show that every relation which is tetradic, pentadic, or of any greater number of correlates is nothing but a compound of triadic relations. It is therefore not surprising to find that beyond the three elements of Firstness, Secondness, and Thirdness, there is nothing else to be found in the phenomenon.” (CP 1.347)

Robert Burch has called Peirce’s ideas of “indecomposability” the ‘Reduction Thesis’ [15]. Peirce was able to prove these points with his form of predicate calculus (first-order logic) and via the logics of his existential graphs.

Once the basic structure of the trichotomy and the nature of its primitives were in place, it was logical for Peirce to generalize the design across many other areas of investigation and research. Because of the signs’ groundings in logic, Peirce’s three main forms of deductive, inductive and abductive logic also flow from the same approach and mindset. Using his broader terminology of the general triad, Peirce writes that when the First and Second [7]:

“. . . are found inadequate, the third is the conception which is then called for. The third is that which bridges over the chasm between the absolute first and last, and brings them into relationship. We are told that every science has its qualitative and its quantitative stage; now its qualitative stage is when dual distinctions — whether a given subject has a given predicate or not — suffice; the quantitative stage comes when, no longer content with such rough distinctions, we require to insert a possible halfway between every two possible conditions of the subject in regard to its possession of the quality indicated by the predicate. Ancient mechanics recognized forces as causes which produced motions as their immediate effects, looking no further than the essentially dual relation of cause and effect. That was why it could make no progress with dynamics. The work of Galileo and his successors lay in showing that forces are accelerations by which [a] state of velocity is gradually brought about. The words “cause” and “effect” still linger, but the old conceptions have been dropped from mechanical philosophy; for the fact now known is that in certain relative positions bodies undergo certain accelerations. Now an acceleration, instead of being like a velocity a relation between two successive positions, is a relation between three. . . . we may go so far as to say that all the great steps in the method of science in every department have consisted in bringing into relation cases previously discrete.” (CP 1.359)

My intuition of the importance of the third part of the triad comes from such terms as perspective, gradation and probability, concepts impossible to capture in a binary world.

Some Observations on the Knowledge Of and Use of the Peircean Triad

C.S. Peirce embraced a realistic philosophy, but also embedded it in a belief that our understanding of the world is fallible and that we needed to test our perceptions via logic. Better approximations of truth arise from questioning using the scientific method (via a triad of logics) and from refining consensus within the community about how (via language signs) we communicate that truth. Peirce termed this overall approach pragmatism; it is firmly grounded in Peirce’s views of logic and his theory of signs. While there is absolute truth, in Peirce’s semiotic process it acts more as a limit, to which our seeking of additional knowledge and clarity of communication with language continuously approximates. Through the scientific method and questioning we get closer and closer to the truth and to an ability to communicate it to one another. But new knowledge may change those understandings, which in any case will always remain proximate [16].

Peirce greatly admired the natural classification systems of Louis Agassiz and used animal lineages in many of his examples. He was a strong proponent of natural classification. Though the morphological basis for classifying organisms in Peirce’s day has been replaced with genetic means, Peirce would surely support this new knowledge, since his philosophy is grounded on a triad of primitive unary, binary and tertiary relations, bound together in a logical sign process seeking truth. Again, Peirce called these Firstness, Secondness, and Thirdness.

Like many of Peirce’s concepts, his ideas of Firstness, Secondness and Thirdness (which I shall hereafter just give the shorthand of ‘Thirdness‘) have proven difficult to grasp, let alone articulate. After a decade of reading and studying Peirce, I think I can point to these factors as making Peirce a difficult nut to crack:

  • First, though most papers that Peirce published during his lifetime are available, perhaps as many as three-quarters of his writings still wait to be transcribed [14];
  • Second, Peirce is a terminology junky, coining and revising terms with infuriating frequency. I don’t think he did this just to be obtuse. Rather, in his focus on language and communications (as signs) he wanted to avoid imprecise or easily confused terms. He often tried to ground his terminology in Greek language roots, and tried to be painfully precise in his use of suffixes and combinations. Witness his use of semeiosis over semiosis, or the replacement of pragmatism with pragmaticism to avoid the misuse he perceived from its appropriation by William James. That Peirce settled on his terminology of Thirdness for his triadic relations signifies its generality and universal applicability;
  • Third, Peirce wrote and refined his thinking over a written historical record of nearly fifty years, which was also a period of the most significant technological changes in human history. Terms and ideas evolved much over this time. His views of categories and signs evolved in a similar manner. In general, revisions in terminology or concepts in his later writings should hold precedence over earlier ones;
  • Fourth, he was active in elaborating his theory of signs to be more inclusive and refined, a work of some 66 putative signs that remained very much incomplete at the time of his death. There has been a bit of a cottage industry in trying to rationalize and elucidate what this more complex sign schema might have meant [17], though frankly much of this learned inspection feels terminology-bound and more like speculation than practical guidance; and
  • Fifth, and possibly most importantly, most Peircean scholarship appears to me to be more literal with an attempt to discern original intent. Many arguments seem fixated on nuance or terminology interpretation as opposed to its underlying meaning or mindset. To put it in Peircean terms, most scholarship of Peirce’s triadic signs seems to be focused on Firstness and Secondness, rather than Thirdness.

The connections of Peirce’s sign theory, his three-fold logic of deduction-induction-abduction, the role he saw for the scientific method as the proper way to understand and adjudicate “truth”, and his really neat ideas about a community of inquiry have all fed my intuition that Peirce was on to some very basic insights. My Aha! moment, if I can elevate it as such, was when I realized that trying to cram these insights into Peirce’s elaborate sign terminology and other literal aspects of his writing were self-defeating. The Aha! arose when I chose rather to try to understand the mindset underlying Peirce’s thinking and the triadic nature of his semiosis. The very generalizations Peirce made himself around the rather amorphous designations of Firstness, Secondness, Thirdness seemed to affirm that what he was truly getting at was a way of thinking, a way of “decomposing” the world, that had universal applicability irrespective of domain or problem.

Thus, in order to make this insight operational, it first was necessary to understand the essence of what lies behind Peirce’s notions of Firstness, Secondness and Thirdness.

An Expanded View of Firstness, Secondness and Thirdness

Peirce’s notions of Thirdness are expressed in many different ways in many different contexts. These notions have been further interpreted by the students of Peirce. In order to get at the purpose of the triadic Thirdness concepts, I thought it useful to research the question in the same way that Peirce recommends. After all, Firstness, Secondness and Thirdness should themselves be prototypes for what Peirce called the “natural classes” [7]:

“The descriptive definition of a natural class, according to what I have been saying, is not the essence of it. It is only an enumeration of tests by which the class may be recognized in any one of its members. A description of a natural class must be founded upon samples of it or typical examples.” (CP 1.223)

The other interesting aspect of Peirce’s Thirdness is how relations between Firstness, Secondness and Thirdness are treated. Because of the sort of building block nature inherent in a sign, not all potential dyadic relations between the three elements are treated equally. According to the ‘qualification rule’, “a First can be qualified only by a first; a Second can be qualified by a First and a Second; and a Third can be qualified by a First, Second, and a Third” [18]. Note that a Third can not be involved in either a First or Second.

Keeping these dynamics in mind, here is my personal library of Thirdness relationships as expressed by Peirce in his own writings, or in the writings of his students. Generally, references to Thirdness are scattered, and to my knowledge no where can one see more than two or three examples side-by-side. The table below is thus “an enumeration of tests by which the class may be recognized in any one of its members” [19]:

Firstness Secondness Thirdness first second third monad dyad triad point line triangle being existence external qualia particularity generality chaos order structure “past” “present” “future” sign object interpretant inheres adheres coheres attribute individual type icon index symbol quality “fact” thought sensation reaction convergence independent relative mediating intension extension information internal external conceptual spontaneity dependence meaning possibility fact law feeling effort habit chance law habit-taking qualities of phenomena actual facts laws (and thoughts) feeling consciousness thought thought-sign connected interpreted possible modality actual modality necessary modality possibles occurrences collections abstractives concretetives collectives descriptives denominatives distributives conscious (feeling) self-conscious mind words propositions arguments terms propositions inferences/syllogisms singular characters dual characters plural characters absolute chance mechanical necessity law of love symbols generality interpreter simples recurrences comprehensions idea (of) kind of existence continuity ideas determination of ideas by
previous ideas determination of ideas by
previous process what is possible what is actual what is necessary hypothetical categorical relative deductions inductions abductions clearness of conceptions clearness of distinctions clearness of practical implications speculative grammar logic and classified arguments methods of truth-seeking phenomenology normative science metaphysics tychasticism anancasticism agapasticism primitives and essences characterizing the objects transformations and reflections what may be what characterizes it what it means complete in itself, freedom, measureless variety, freshness, multiplicity, manifold of sense, peculiar, idiosyncratic, suchness idea of otherness, comparison, dichotomies, reaction, mutual action, will, volition, involuntary attention, shock, sense of change idea of composition, continuity, moderation, comparative, reason, sympathy, intelligence, structure, regularities, representation Examples from Research and the Literature of Firstness, Secondness, Thirdness

The best way to glean meaning from this table is through some study and contemplation.

Because these examples are taken from many contexts, it is important to review this table on a row-by-row basis when investigating the nature of ‘Thirdness’. Review of the columns helps elucidate the “natural classes” of Firstness, Secondness and Thirdness. Some items appear in more than one column, reflecting the natural process of semiosis wherein more basic concepts cascade to the next focus of semiotic attention. The last row is a kind of catch-all trying to capture other mentions of Thirdness in Peirce’s phenomenology.

The table spans from the fully potential or abstract, such as “first” or “third”, to entire realms of science or logic. This spanning of scope reflects the genius of Peirce’s insight wherein semiosis can begin literally at the cusp of Nothingness [20] and then proceed to capture the process of signmaking, language, logic, the scientific method and thought abstraction to embrace the broadest and most complex of topics. This process is itself mediated by truth-testing and community use and consensus, with constant refinement as new insights and knowledge arise.

Reviewing these trichotomies affirms the fulsomeness of Peirce’s semiotic model. Further, as Peirce repeatedly noted, there are no hard and fast boundaries between these categories [21]. Forces of history or culture or science are complex and interconnected in the extreme; trying to decompose complicated concepts into their Thirdness is a matter of judgment and perspective. Peirce, however, was serene about this, since the premises and assignments resulting from such categorizations are (ultimately) subject to logical testing and conformance with the observable, real world.

The ‘Thirdness’ Mindset Applied to Categorization

Our excursion into Peirce’s foundational, triadic view was driven by pragmatic needs. Structured Dynamics‘ expertise in knowledge-based artificial intelligence (KBAI) benefits from efficient and coherent means to represent knowledge. The data models and organizational schema underlying KR should be as close as possible to the logical ways the world is structured and perceived. A key aspect of that challenge is how to define a grammar and establish a logical structure for representing knowledge. Peirce’s triadic approach and mindset have come to be, in my view, essential foundations to that challenge.

As before, we will again let Peirce’s own words guide us in how to approach the categorization of our knowledge domains. Let’s first address the question of where we should direct attention. How do we set priorities for where our categorization attention should focus? [7]:

“Taking any class in whose essential idea the predominant element is Thirdness, or Representation, the self development of that essential idea — which development, let me say, is not to be compassed by any amount of mere “hard thinking,” but only by an elaborate process founded upon experience and reason combined — results in a trichotomy giving rise to three sub-classes, or genera, involving respectively a relatively genuine thirdness, a relatively reactional thirdness or thirdness of the lesser degree of degeneracy, and a relatively qualitative thirdness or thirdness of the last degeneracy. This last may subdivide, and its species may even be governed by the three categories, but it will not subdivide, in the manner which we are considering, by the essential determinations of its conception. The genus corresponding to the lesser degree of degeneracy, the reactionally degenerate genus, will subdivide after the manner of the Second category, forming a catena; while the genus of relatively genuine Thirdness will subdivide by Trichotomy just like that from which it resulted. Only as the division proceeds, the subdivisions become harder and harder to discern.” (CP 5.72)

The way I interpret this (in part) is that categories in which new ideas or insights have arisen — themselves elements of Thirdness for that category — are targets for new categorization. That new category should focus on the idea or insight gained, such that each new category has a character and scope different from the one that spawned it. Of course, based on the purpose of the KBAI effort, some ideas or insights have larger potential effect on the domain, and those should get priority attention. As a practical matter this means that categories of more potential importance to the sponsor of the KBAI effort receive the most focus.

Once a categorization target has been chosen, Peirce also put forward some general execution steps [7]:

“. . . introduce the monadic idea of »first« at the very outset. To get at the idea of a monad, and especially to make it an accurate and clear conception, it is necessary to begin with the idea of a triad and find the monad-idea involved in it. But this is only a scaffolding necessary during the process of constructing the conception. When the conception has been constructed, the scaffolding may be removed, and the monad-idea will be there in all its abstract perfection. According to the path here pursued from monad to triad, from monadic triads to triadic triads, etc., we do not progress by logical involution — we do not say the monad involves a dyad — but we pursue a path of evolution. That is to say, we say that to carry out and perfect the monad, we need next a dyad. This seems to be a vague method when stated in general terms; but in each case, it turns out that deep study of each conception in all its features brings a clear perception that precisely a given next conception is called for.” (CP 1.490)

We are basing this process of categorization upon the same triadic design noted above. However, now that our context is categorization, the nature of the triad is different than that for the basic sign, as the similar figure to the right attests.

The area of the Secondness is where we surface and describe the particular objects or elements that define this category. Peirce described it thus [7]:

“So far Hegel is quite right. But he formulates the general procedure in too narrow a way, making it use no higher method than dilemma, instead of giving it an observational essence. The real formula is this: a conception is framed according to a certain precept, [then] having so obtained it, we proceed to notice features of it which, though necessarily involved in the precept, did not need to be taken into account in order to construct the conception. These features we perceive take radically different shapes; and these shapes, we find, must be particularized, or decided between, before we can gain a more perfect grasp of the original conception. It is thus that thought is urged on in a predestined path. This is the true evolution of thought, of which Hegel’s dilemmatic method is only a special character which the evolution is sometimes found to assume.” (CP 1.491)

In Thirdness we are contemplating the category, thinking about it, analyzing it, using and gaining experience with it, such that we can begin to see patterns or laws or “habits” (as Peirce so famously put it) or new connections and relationships with it. The ideas and insights (and laws or standardizations) that derive from this process are themselves elements of the category’s Thirdness. This is where new knowledge arises or purposes are fulfilled, and then subsequently split and codified as new signs useful to the knowledge space.

As domains are investigated to deeper levels or new insights expand the branches of the knowledge graph, each new layer is best tackled via this three-fold investigation. Of course, context requires its own perspectives and slices; the listing of Thirdness options provided above can help stimulate these thoughts.

Using Peirce’s labels, but my own diagram, we can show the categorization process as having some sequential development:

But, of course, interrelationships adhere to the Peircean Thirdness and there continues to be growth and additions. Categories thus tend to fill themselves up with more insights and ideas until such time as the scope and diversity compel another categorization. In these ways categorization is not linear, but accretive and dynamic.

Like our investigations of the broad idea of Thirdness above, there are some Firstness, Secondness, and Thirdness aspects of how to think about the idea of categorization. I use this kind of mental checklist when it comes time to split a concept or category into a new categorization:

Firstness Secondness Thirdness Symbols idea of; nature of; milieu;
“category potentials” reference concepts standards Generality cross-products of Firstness language (incl. domain); computational analysis; representation; continua Interpreters
(human or machine) What are the ingredients, ideas, essences of the category? What are the new things or relationships of the category? What are the laws, practices, outputs arising from the category? General Thoughts on Using ‘Thirdness’ for Categorization

The essential point is to break free from Peirce’s often stultifying terminology and embrace the mindset behind Thirdness. Categorization, or any other knowledge representation task for that matter, can be approached logically and, yes, systematically.

The Perspective of Thirdness

Just as perspective does not occur without Thirdness, I think we will see Peirce’s contributions make a notable difference in how knowledge representation efforts move forward. A driver of this change is knowledge-based artificial intelligence. I feel like problems and questions that have stymied me for decades are lifting like so much fog as I embrace the Peircean Thirdness mindset. I think that it is possible to codify and train others to use this mindset, which is really but a specialized application of Peirce’s overall conception of semiosis [22].

Twenty five years ago Nathan Houser opined that “. . . a sound and detailed extension of Peirce’s analysis of signs to his full set of ten divisions and sixty-six classes is perhaps the most pressing problem for Peircean semioticians” [23]. I agree with the sense of this opinion, but the ten divisions and sixty-six classes are a sign classification; the greater primitive for Peirce’s thinking is the triad and his application of it across all domains of discourse. This is the better grounding for understanding Peirce.

John Sowa, mentioned in the intro, also put forward a knowledge representation, which he partially attributed to Peirce [2,4], and included the three basic elements of the sign triad. But Sowa did not infuse his design with the Peircean triad, with the amalgam criticized for its lack of coherency [11]. Peircean ideas have also informed computational approaches [24] and language parsing [25]. Nonetheless, despite important Peircean ideas and contributions across the knowledge representation spectrum, I have been unable to find any upper ontology or vocabulary based on Thirdness. Terminology can get in the way.

In the intro, I mentioned my epiphany from specifics to mindset in Peirce’s teachings. This insight has not caused me to suddenly understand everything Peirce was trying to say, nor to come to some new level of consciousness. However, what it has done is to open a door to a new way of thinking and looking at the world. I am now finding prior, knotty problems of categorization and knowledge representation are becoming (more) tractable. I am excited and eager to look at some problems that have stymied me for years. Many of these problems, such as how to model events, situations, identity, representation, and continuity or characterization through time, may sound like philosophers’ mill stones, but they often lie at the heart of the most difficult problems in knowledge modeling and representation. Even the tiniest break in the mental and conceptual logjams around such issues feels like major progress. For that, I thank Peirce’s triads.

[1] See Sowa’s Web site, especially the sections on ontology, knowledge representation, and publications. [2] See, for example, John F. Sowa, 2000. “Ontology, Metadata, and Semiotics,” presented at ICCS 2000 in Darmstadt, Germany, on August 14, 2000; published in B. Ganter & G. W. Mineau, eds., Conceptual Structures: Logical, Linguistic, and Computational Issues, Lecture Notes in AI #1867, Springer-Verlag, Berlin, 2000, pp. 55-81. May be found at http://www.jfsowa.com/ontology/ontometa.htm. Also see John F. Sowa, 2006. “Peirce’s Contributions to the 21st Century,” presented at International Conference on Conceptual Structures, Aalborg, Denmark, July 17, 2006; and [4] below. [3] I have written a number of pieces based primarily around Peirce’s insights; see, for example, http://www.mkbergman.com/category/peircean-principles/. [4] John F. Sowa, 2001. “Signs, Processes, and Language Games: Foundations for Ontology,” in Proceedings of the 9th International Conference On Conceptual Structures, ICCS’01. 2001. [5] Peirce actually spelled his approach as semeiosis, but I use the simpler version here. See also separate discussion of pragmaticism. [6] For example, Peirce said [7]: “Thought is not necessarily connected with a brain. It appears in the work of bees, of crystals, and throughout the purely physical world; and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there.” (CP 4.551). At first this seems rather strange. However, “thought” for Peirce in this context is the notion of the process by which the sign is recognized and interpreted. See also [20]. [7] See the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208. [8] Also see, for example, the use of trichotomies in philosophy or some of the nature of three in mathematics or religion. [9] J. Locke, 1690. “An Essay Concerning Human Understanding”, Book II, Chapter XXXIII. Reprinted, 1964: 249. John Y. Yolton, Ed. Dutton. New York, NY. [10] See http://www.webofstories.com/play/marvin.minsky/111. [11] Ludger Jansen, 2008. “Categories: The Top-level Ontology,” Applied ontology: An introduction (2008): 173-196. [12] Nicola Guarino, 1997. “Some Organizing Principles For A Unified Top-Level Ontology,” National Research Council, LADSEB-CNR Int. Report, V3.0, August 1997  [13] P. Farias and J. Queiroz, 2003. “On Diagrams for Peirce’s 10, 28, and 66 Classes of Signs“, Semiotica 147(1/4), pp.165-184. [14] Spencer Case, 2014. “The Man with a Kink in His Brain,” from online National Review, July 21, 2014. “Over the course of Peirce’s life, that kinky brain produced a total of about 12,000 printed pages and 80,000 handwritten pages. The Peirce Edition Project, founded in 1976, is still organizing and editing the massive Peirce corpus. So far, Indiana University Press has published seven volumes of his writings — of an expected thirty.” [15] Robert Burch has called Peirce’s ideas of “indecomposability” the ‘Reduction Thesis’; see Robert Burch, 1991. A Peircean Reduction Thesis: The Foundations of Topological Logic, Texas Tech University Press, Lubbock, TX. Peirce’s reduction thesis is never stated explicitly by Peirce, but is alluded to in numerous snippets. The basic thesis is that ternary relations suffice to construct arbitrary relations, but that not all relationscan be constructed from unary and binary relations alone. [16] M.K. Bergman, 2016. “Re-thinking Knowledge Representation,” AI3:::Adaptive Information blog, March 14, 2016. [17] Amongst many, see, for example, Janos J. Sarbo and József I. Farkas, 2013. “Towards Meaningful Information Processing: A Unifying Representation for Peirce’s Sign Types,” Signs-International Journal of Semiotics 7 (2013): 1-44. In that article, the authors state: ” . . . our model has the potential of representing three types of relation, consisting of 10, 28, and 66 elements, that are analogous to Peirce’s three classifications of signs. This implies the possibility of a common representation for Peirce’s different classifications.. . . By virtue of the above relation with Peircean semiotics, and because of the fundamental nature of signs, our approach has the potential for a uniform modeling of information processing in any domain, theoretically.” Two other researchers of Peircean signs are, for example, P. Farias and J. Queiroz, 2003. “On Diagrams for Peirce’s 10, 28, and 66 Classes of Signs”, Semiotica 147(1/4), pp.165-184. Also, the Web site Minute Semiotic is dedicated to one interpretation of Peirce’s signs, including interactive descriptions (from the author’s perspective) of the 66 Peircean signs. [18] David Savan, 1987-1988. “An Introduction to C.S.Peirce’s Full System of Semeiotic,” Monograph Series of the Toronto Semiotic Circle. Vol. 1.  [19] Table sources and the order of presentation very roughly move from the primitive to the more complex and elaborative. [20] The idea of Firstness may range from something like an energetic input that causes chemicals to combine into a new structured form or ordered state to something like a new recognition in the mind occasioned by a flick of the eye or a shifting thought. The representamen is merely a potential sign until it is energized or intrudes on consciousness, wherein the object is now made apparent as interpreted. The process of reifying the sign itself produces a new reality, its Thirdness, which can then become a subject of the sign-recognizing process in its own right. In this regard, Peirce was formulating a theory of signs that could describe how more order may occur in the world, including the formation and evolution of the cosmos and the initial origins of life. [21] As one example, Peirce states [7]: “. . . it may be quite impossible to draw a sharp line of demarcation between two classes, although they are real and natural classes in strictest truth. Namely, this will happen when the form about which the individuals of one class cluster is not so unlike the form about which individuals of another class cluster but that variations from each middling form may precisely agree.” (Peirce CP 1.208) [22] Semiosis has been viewed my many as applicable to a wide variety of domains such as animal calls and language, the chemical and energetic origin of life, evolution, and language analysis and parsing. The linkage of these ideas to Peirce results from his statement such as [7]: “Thought is not necessarily connected with a brain. It appears in the work of bees, of crystals, and throughout the purely physical world; and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there. . . . Not only is thoughtin the organic world, but it develops there.” (Peirce CP 4.551) [23] Nathan Houser, 1992. “On Peirce’s Theory of Propositions: A Response to Hilpinen.” Transactions of the Charles S. Peirce Society 28, no. 3 (1992): 489-504. [24] See, for example, Gary Richmond’s trikonic approach: Gary Richmond, 2005. “Outline of trikonic Diagrammatic Trichotomic,” in: F. Dau, M.L. Mugnier, and G. Tumme, ed., Conceptual Structures: Common Semantics for Sharing Knowledge: 13th International Conference on Conceptual Structures, ICCS 2005, Kassel, Germany, 17–22 July 2005. Springer-Verlag GmbH, pp. 453 – 466. [25] See, for example, one of the earlier examples, John F. Sowa, 1991. “Toward the Expressive Power of Natural Language.” Principles of Semantic Networks (1991): 157-189.

Re-thinking Knowledge Representation

AI3:::Adaptive Information (Mike Bergman) - Mon, 03/14/2016 - 17:15
A New Era in Artificial Intelligence Will Open Pandora’s Box

Here’s a prediction: the new emphasis on artificial intelligence and robotics will occasion some new looks at knowledge representation. Prior to the past few years many knowledge representation (KR) projects have been more in the way of prototypes or games. But, now that we are seeing real robotics and knowledge-based AI activities take off, some of the prior warts and problems of leading KR approaches are starting to become evident.

For example, for years major upper-level ontologies have tended to emphasize dichotomous splits in how to “model” the world, including:

  • abstract-physical — a split between what is fictional or conceptual and what is tangibly real
  • occurrent-continuant — a split between a “snapshot” view of the world and its entities versus a “spanning” view that is explicit about changes in things over time
  • perduant-endurant — a split for how to regard the identity of individuals, either as a sequence of individuals distinguished by temporal parts (for example, childhood or adulthood) or as the individual enduring over time
  • dependent-independent — a split between accidents (which depend on some other entity) and substances (which are independent)
  • particulars-universals — a split between individuals in space and time that cannot be attributed to other entities versus abstract universals such as properties that may be assigned to anything
  • determinate-indeterminate.

Since the mid-1980s, description logics have also tended to govern most KR languages, and are the basis of the semantic Web data model and languages of RDF and OWL. (However, common logic and its dialects are also used as a more complete representation of first-order logic.) The trade-off in KR language design is one of expressiveness versus complexity.

Cyc was developed as one means to address a gap in standard KR approaches: how to capture and model common sense. Conceptual graphs, formally a part of common logic, were developed to handle n-ary relationships and the questions of sign processes (semiosis), fallibility and processes of pragmatic learning.

Zhou offers a new take on an old strategy to KR, which is to use set theory as the underlying formalism [1]. This first paper deals with the representation itself; a later paper is planned on reasoning.

We do not live in a dichotomous world. And, I personally find Charles Peirce’s semeiosis to be a more compelling grounding for what a KR design should look like. But as Zhou points out, and is evident in current AI advances, robotics and the need for efficient, effective reasoning are testing today’s standards in knowledge representation as never before. I suspect we are in for a period of ferment and innovation as we work to get our KR languages up to task.

[1] Yi Zhou, 2016. “A Set Theoretic Approach for Knowledge Representation: the Representation Part,” arXiv:1603.03511, 14 Mar 2016.

How Fine Grained Can Entity Types Get?

AI3:::Adaptive Information (Mike Bergman) - Tue, 03/08/2016 - 21:00

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A Typology Design Aids Continuous, Logical Typing

Entity recognition or extraction is a key task in natural language processing and one of the most common uses for knowledge bases. Entities are the unique, individual things in the world, and are also sometimes used to characterize some concepts [1]. Context plays an essential role in entity recognition. In general terms we may refer to a thing such as a camera; but a photographer may want more fine-grained distinctions such as SLR cameras or further sub-types like digital SLR cameras or even specific models like the Canon EOS 7D Mark II or even the name of the photographer’s favorite camera, such as ‘Shutter Sue‘. Capitalized names (as is the reference source for named entity recognition) often signals we are dealing with a true individual entity, but again, depending on context, a named automobile such as Chevy Malibu may refer to a specific car or to the entire class of Malibu cars.

The “official” practice of named entity recognition began with the Message Understanding Conferences, especially MUC-6 and MUC-7, in 1995 and 1997. These conferences began competitions for finding “named entities” as well as the practice of in-line tagging [2]. Some of these accepted ‘named entities‘ are also written in lower case, with examples such as rocks (‘gneiss’) or common animals or plants (‘daisy’) or chemicals (‘ozone’) or minerals (‘mica’) or drugs (‘aspirin’) or foods (‘sushi’) or whatever. Some deference was given to the idea of Kripke’s “rigid designators” as providing guidance for how to identify entities; rigid designators include proper names as well as certain natural kinds of terms like biological species and substances. Because of these blurrings, the nomenclature of “named entities” began to fade away. Some practitioners still use the term of named entities, though for some of the reasons outlined in this paper, Structured Dynamics prefers simply to use entity.

Much has changed in the twenty years since the seminal MUC conferences regarding entity recognition and characterization. We are learning to adopt a very fine-grained approach to entity types and a typology design suited to interoperating (“bridging”) over a broad range of viewpoints and contexts. Most broadly, the idea of fine-grained entity types has led us to a logically grounded typology design.

The Growing Trend to Fine-Grained Entity Types

Beginning with the original MUC conferences, the initial entity types tested and recognized were for person, organization, and location names [3]. However, it did not take long for various groups and researchers to want more entity types, more distinctions. BBN categories, proposed in 2002, were used for question answering and consisted of 29 types and 64 subtypes [4]. Sekine put forward and refined over many years his Extended Entity Types, which grew to about 200 types [5], as shown in this figure:

Sekine Extended Entity Types

These ideas of extended entity types helped inform a variety of tagging services over the past decade, notably including OpenCalais, Zemanta, AlchemyAPI, and OpenAmplify, among others. Moreover the research community also expanded its efforts into more and more entity types, or what came to be known as fine-grained entities [6].

Some of these produced more formal organizations of entity type classifications. This one, from Ling and Weld proposed 112 entity types in 2012 [7]:

Ling 112 Entity Types

Another one, from Gillick et al. in 2014 proposed 86 entity types [8], organized, in part, according to the same person, organization, and location types from the earliest MUC conferences:

Gillick 86 Entity Types

These efforts are also notable because machine learners have been trained to recognize the types shown. What entity types are covered, the different conceptions of the world, and how to organize entity types varies broadly across these references.

The complement to entity extraction for unstructured text is to label the text in the first place. For this, a number of schema presently exist that provide vocabularies of entity types and standard means for tagging text. These include:

  • DBpedia Ontology: 738 types [9]
  • schema.org: 636 types [10]
  • YAGO: 505 types; see also HYENA [11]
  • GeoNames: 654 “feature codes” [12]

In Structured Dynamics’ own work, we have mapped the UMBEL knowledge graph against Wikipedia content and found that 25,000 nodes, or more than 70 percent of its 35,000 reference concepts, correspond to entity types [13]. These mappings provide typing connections for millions of Wikipedia articles. The typing and organization of entity types thus appears to be of enormous importance in modeling and leveraging the use of knowledge bases.

When we track the coverage of entity types over the past two decades we see logarithmic growth [13]:

Growth in Recognition of Entity Types

This growth in entity types comes from wanting to describe and organize things with more precision. Tagging and extracting structured information from text are obviously a key driver. Yet, for a given enterprise, what is of interest — and at what depth — for a particular task varies widely.

The fact that knowledge bases, such as Wikipedia (but, the lesson applies to domain-specific ones as well), can be supported by entity-level information for literally thousands of entity types means that rich information is available for driving the finest of fine-grained entity extractors. To leverage this raw, informational horsepower it is essential to have a grounded understanding of what an entity is, how to organize them into logical types, and an intensional understanding of the attributes and characteristics that allow inferencing to be conducted over these types. These understandings, in turn, point to the features that are useful to machine learners for artificial intelligence. These understandings also can inform a flexible design for accommodating entity types from coarse- to fine-grained, with variable depth depending on the domain of interest.

Natural Classes and Typologies

We take a realistic view of the world. That is, we believe that what we perceive in the world is real — it is not just a consequence of what we perceive and can be aware of in our minds [14] — and that there are forces and relationships in the world independent of us as selves. Realism is a longstanding tradition in philosophy that extends back to Aristotle and embraces, for example, the natural classification systems of living things as espoused by taxonomists such as Agassiz and Linnaeus.

Charles Sanders Peirce, an American logician and scientist of the late 19th and early 20th centuries, embraced this realistic philosophy but also embedded it in a belief that our understanding of the world is fallible and that we needed to test our perceptions via logic (the scientific method) and shared consensus within the community. His overall approach is known as pragmatism and is firmly grounded in his views of logic and his theory of signs (called semiotics or semeiotics). While there is absolute truth, it actually acts more as a limit, to which our seeking of additional knowledge and clarity of communication with language continuously approximates. Through the scientific method and questioning we get closer and closer to the truth and to an ability to communicate it to one another. But new knowledge may change those understandings, which in any case will always remain proximate.

Peirce’s own words can better illustrate his perspective [15], some of which I have discussed elsewhere under his idea of “natural classes” [16]:

“Thought is not necessarily connected with a brain. It appears in the work of bees, of crystals, and throughout the purely physical world; and one can no more deny that it is really there, than that the colors, the shapes, etc., of objects are really there.” (Peirce CP 4.551)

“What if we try taking the term “natural,” or “real, class” to mean a class of which all the members owe their existence as members of the class to a common final cause? This is somewhat vague; but it is better to allow a term like this to remain vague, until we see our way to rational precision.” (Peirce CP 1.204)

“. . . it may be quite impossible to draw a sharp line of demarcation between two classes, although they are real and natural classes in strictest truth. Namely, this will happen when the form about which the individuals of one class cluster is not so unlike the form about which individuals of another class cluster but that variations from each middling form may precisely agree.” (Peirce CP 1.208)

“When one can lay one’s finger upon the purpose to which a class of things owes its origin, then indeed abstract definition may formulate that purpose. But when one cannot do that, but one can trace the genesis of a class and ascertain how several have been derived by different lines of descent from one less specialized form, this is the best route toward an understanding of what the natural classes are.” (Peirce CP 1.208)

“The descriptive definition of a natural class, according to what I have been saying, is not the essence of it. It is only an enumeration of tests by which the class may be recognized in any one of its members. A description of a natural class must be founded upon samples of it or typical examples.” (Peirce CP 1.223)

“Natural classes” thus are a testable means to organize the real objects in the world, the individual particulars of what we call “entities”. In Structured Dynamics’ usage, we define an entity as something that is an individual object, either real or mental such as an idea, either a part or a whole, and that has:

  • identity, which can be referred to via symbolic names
  • context in relation to other objects, and
  • characteristic attributes, with some expressing the essence of what type of object it is.

The key to classification of entities into categories (or “types” as we use herein) is based on this intensional understanding of attributes. Further, Peirce was expansive in his recognition of what kinds of objects could be classified, specifically including ideas, with application to areas such as social classes, man-made objects, the sciences, chemical elements and living organisms [17]. Again, here are some of Peirce’s own words on the classification of entities [15]:

“All classification, whether artificial or natural, is the arrangement of objects according to ideas. A natural classification is the arrangement of them according to those ideas from which their existence results.” (Peirce CP 1.231)

“The natural classification of science must be based on the study of the history of science; and it is upon this same foundation that the alcove-classification of a library must be based.” (Peirce CP 1.268)

“All natural classification is then essentially, we may almost say, an attempt to find out the true genesis of the objects classified. But by genesis must be understood, not the efficient action which produces the whole by producing the parts, but the final action which produces the parts because they are needed to make the whole. Genesis is production from ideas. It may be difficult to understand how this is true in the biological world, though there is proof enough that it is so. But in regard to science it is a proposition easily enough intelligible. A science is defined by its problem; and its problem is clearly formulated on the basis of abstracter science.” (Peirce CP 1.227)

A natural classification system is one, then, that logically organizes entities with shared attributes into a hierarchy of types, with each type inheriting attributes from its parents and being distinguished by what Peirce calls its final cause, or purpose. This hierarchy of types is thus naturally termed a typology.

An individual that is a member of a natural class has the same kinds of attributes as other members, all of which share this essence of the final cause or purpose. We look to Peirce for the guidance in this area because his method of classification is testable, based on discernable attributes, and grounded in logic. Further, that logic is itself grounded in his theory of signs, which ties these understandings ultimately to natural language.

Logic and the Typology Design

Unlike more interconnected knowledge graphs (which can have many network linkages), typologies are organized strictly along these lines of shared attributes, which is both simpler and provides an orthogonal means for investigating type class membership. Further, because the essential attributes or characteristics across entities in an entire domain can differ broadly — such as living v inanimate things, natural things v man-made things, ideas v physical objects, etc. — it is possible to make disjointedness assertions between entire groupings of natural entity classes. Disjoint assertions combined with logical organization and inference mean a typology design that lends itself to reasoning and tractability.

The idea of nested, hierarchical types organized into broad branches of different entity typologies also provides a very flexible design for interoperating with a diversity of world views and degrees of specificity. The photographer, as I discussed above, is interested in different camera types and even how specific cameras can relate to a detailed entity typing structure. Another party more interested in products across the board may have a view to greater breadth, but lesser depth, about cameras and related equipment. A typology design, logically organized and placed into a consistent grounding of attributes, can readily interoperate with these different world views.

A typology design for organizing entities can thus be visualized as a kind of accordion or squeezebox, expandable when detail requires, or collapsed to more coarse-grained when relating to broader views. The organization of entity types also has a different structure than the more graph-like organization of higher-level conceptual schema, or knowledge graphs. In the cases of broad knowledge bases, such as UMBEL or Wikipedia, where 70 percent or more of the overall schema is related to entity types, more attention can now be devoted to aspects of concepts or relations.

The idea that knowledge bases can be purposefully crafted to support knowledge-based artificial intelligence, or KBAI, flows from these kinds of realizations. We begin to see that we can tease out different aspects of a knowledge base, each with its own logic and relation to the other aspects. Concepts, entities, attributes and relations — including the natural classes or types that can logically organize them — all deserve discrete attention and treatment.

Peirce’s consistent belief that the real world can be logically conceived and organized provides guidance for how we can continue to structure our knowledge bases into computable form. We now have a coherent base for treating entities and their natural classes as an essential component to that thinking. We can continue to be more fine-grained so long as there are unique essences to things that enable them to be grouped into natural classes.

[1] The role for the label “entity” can also refer to what is known as the root node in some systems such as SUMO (see also http://virtual.cvut.cz/kifb/en/toc/229.html). In the OWL language and RDF data model we use, the root node is known as “thing”. Clearly, our use of the term “entity” is much different than SUMO and resides at a subsidiary place in the overall TBox hierarchy. In this case, and frankly for most semantic matches, equivalences should be judged with care, with context the crucial deciding factor. [2] N. Chinchor, 1997. “Overview of MUC-7,” MUC-7 Proceedings, 1997. [3] While all of these are indeed entity types, the early MUCs also tested dates, times, percentages, and monetary amounts. [4] Ada Brunstein, 2002. “Annotation Guidelines for Answer Types”. LDC Catalog, Linguistic Data Consortium. Aug 3, 2002. [5] See the Sekine Extended Entity Types; the listing also includes attributes info at bottom of source page. [6] For example, try this query, https://scholar.google.com/scholar?q=”fine-grained+entity”, also without quotes. [7] Xiao Ling and Daniel S. Weld, 2012. “Fine-Grained Entity Recognition,” in AAAI. 2012. [8] Dan Gillick, Nevena Lazic, Kuzman Ganchev, Jesse Kirchner, and David Huynh, 2104. “Context-Dependent Fine-Grained Entity Type Tagging,” arXiv preprint arXiv:1412.1820 (2014). [9] Christian Bizer, Jens Lehmann, Georgi Kobilarov, Sören Auer, Christian Becker, Richard Cyganiak, and Sebastian Hellmann, 2009. “DBpedia-A Crystallization Point for the Web of Data.” Web Semantics: science, services and agents on the world wide web 7, no. 3 (2009): 154-165; 170 classes in this paper. That has grown to more than 700; see http://mappings.dbpedia.org/server/ontology/classes/ and http://wiki.dbpedia.org/services-resources/datasets/dataset-2015-04/dataset-2015-04-statistics. [10] The listing is under some dynamic growth. This is the official count as of September 8, 2015, from http://schema.org/docs/full.html. Current updates are available from Github. [11] Joanna Biega, Erdal Kuzey, and Fabian M. Suchanek, 2013. “Inside YAGO2: A Transparent Information Extraction Architecture,” in Proceedings of the 22nd international conference on World Wide Web, pp. 325-328. International World Wide Web Conferences Steering Committee, 2013. Also see Mohamed Amir Yosef, Sandro Bauer, Johannes Hoffart, Marc Spaniol, Gerhard Weikum, 2012. “HYENA: Hierarchical Type Classification for Entity Names,” in Proceedings of the 24th International Conference on Computational Linguistics, Coling 2012, Mumbai, India, 2012. [12] See https://en.wikipedia.org/wiki/GeoNames. [13] This figure and some of the accompanying text comes from a prior article, M.K. Bergman, “Creating a Platform for Machine-based Artificial Intelligence“, AI3:::Adaptive Information blog, September 21, 2015. [14] Realism is often contrasted to idealism, nominalism or conceptualism, wherein how the world exists is a function of how we think about or name things. Descartes, for example, summarized his conceptualist view with his aphorism “I think, therefore I am.” [15] See the electronic edition of The Collected Papers of Charles Sanders Peirce, reproducing Vols. I-VI, Charles Hartshorne and Paul Weiss, eds., 1931-1935, Harvard University Press, Cambridge, Mass., and Arthur W. Burks, ed., 1958, Vols. VII-VIII, Harvard University Press, Cambridge, Mass. The citation scheme is volume number using Arabic numerals followed by section number from the collected papers, shown as, for example, CP 1.208. [16] M.K. Bergman, 2015. “‘Natural’ Classes in the Knowledge Web“, AI3:::Adaptive Information blog, July 13, 2015. [17] See, for example, Menno Hulswit, 2000. “Natural Classes and Causation“, in the online Digital Encyclopedia of Charles S. Peirce.
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