This last part on the updated KBpedia grammar is the final advance article on the knowledge graph prior to the release of version 1.50. In this article, I update and summarize the grammar at the heart of the ontology. I have written previously  on the role that Charles Sanders Peirce gave to what he called a speculative grammar, a Firstness in his triadic view of semiosis, or the logic of signs. The basic idea of a 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? Of course, in our context, the domain of inquiry is the representation of knowledge in a knowledge graph useful to knowledge-based artificial intelligence, or KBAI.
Here is how Peirce in his own words placed speculative grammar in relation to his theory of logic :
“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)
As I stated in an earlier article on a speculative grammar :
“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.”
As Peirce says in his Logic of Relatives paper :
“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)
He goes on to say that the “. . . the woof and warp of a thought and all research is symbols, and the life of thought and science is the life inherent in symbols; so that it is wrong to say that a good language is important to good thought, merely; for it is of the essence of it.” (CP 2.220) An understanding of this language for KBpedia is essential to appreciate what the knowledge graph does and how to use it.
The Grammar Begins with the Universal Categories
The upper structure of KBpedia is captured by the KBpedia Knowledge Ontology. KKO is informed by the triadic logic and basic (“universal”) categories of C.S. Peirce. These same triadic universal categories are also the basis for Peirce’s semiosis, which both captures his views on the nature of logic and the basis of signs in representation and communication. These three universal constituents of Peirce’s trichotomy were in his view the most primitive or reduced manner by which to understand and categorize things, concepts and ideas. A key point for our purposes is that ‘threes’ are the fewest by which to model context and perspective, essential to capture the nature of knowledge .
Peirce’s trichotomy of the universal categories can be roughly summarized as:
- Firstness [1ns] — these are possibilities or potentials, the basic forces or qualities that combine together or interact in various ways to enable the real things we perceive in the world, such as matter, life and ideas. These are the unrealized building blocks, or primitives, the essences or attributes or possible juxtapositions
- Secondness [2ns] — these are the particular realized things or concepts in the world, what we can perceive, point to and describe. A particular is also known as an entity, event, instance or individual
- Thirdness [3ns] — these are the laws, habits, regularities and continuities that may be generalized from particulars. All generals — what are also known as classes, kinds or types — belong to this category. The process of finding and deriving these generalities also leads to new insights or emergent properties, which continue to fuel knowledge discovery. Insights arising from Thirdness enable us to further explore and understand things, and is a driving force for further categorization.
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.
KKO begins with these three universal categories, all subsumed under the standard
owl:Thing root node (a convention when using OWL). The first Firstness of KKO is called the Monad branch. This branch represents the qualities or potentials or possibilities that help define the actual individual things in the ontology, or Particulars, the real entities or events in the ontology. Monads are attributes and similar, such as colors or shapes; they do not exist independently except as concepts or ideas of themselves. They are only embodied when in relation to a specific instance. Particulars, or instances, are the second branch, which is the first Secondness. Particulars are the real individual things of the ontology. The largest branch in terms of nodes for KKO is the third one, the Generals (also called SuperTypes), wherein the general kinds, classes or types of the ontology are located. Generals are where generalizations (or categorizations) of individual things are made into types or classes. The idea of a man (as a representation of male humans) or the idea of a camera (as a representation of devices to capture an image) are generals. In Peircean terms, generals are as real as particulars, even though they are not instantiated into an individual thing. Generals are the largest category in terms of conceptual or classificatory richness in KKO.
Most layers of the the upper KKO are themselves split into threes, with the same ideas of Firstness, Secondness and Thirdness applied to the categories at each level. Categorization is itself a process grounded in these senses of the universal categories. Whenever an anomalous fact is discovered or the scale of a given category gets too large, it is time to create a new category with its own terminology (grammar), instances and generalities. It is through the application of this Peircean mindset that the breadth and scope of the knowledge graph may be grown.
Each level of the KKO may be labeled as to whether its given category is one of Firstness (1, or 1ns), Secondness (2, or 2ns), or Thirdness (3, or 3ns). We can here see the full upper structure of KKO, with its some 170 concepts, each one labeled as to which of the universal categories applies:
Unfortunately, the graphing software used does not order the nodes by Firstness (1), Secondness (2) or Thirdness (3). (A demo version, viewable in Protege, is labeled such that this ordering is maintained; it will be made available upon KBpedia v 1.50’s release.)
The KKO structure enables us to capture the ideas of constituents and building blocks under the Monads; to place individual instances of entities and events under Particulars; and to generalize or find natural consistencies amongst kinds (or classes) under the Generals. There tends to be some conceptual parallelisms in this structure. The idea about a quality or relation may be placed as an abstract consideration under Monads; an embodied or instantiated quality or relation may be placed as an individual instance under Particulars; or a generalization (or “law”) about such qualities or relations may be placed under Generals. We can reason across all branches and levels of this structure, which means we can reason over things like colors and attributes and relations as easily as types. There is no object or concept, real or imaginary, historical or in the future, which can not be placed into this knowledge representation (KR) structure.
More than 85% of the classificatory structure of KBpedia resides in the generals, or types. These, in turn, are organized according to a set of typologies, or natural classification structures. (The tie-in points to these typologies are shown in the structure above, but the actual typology structures are not.) Unlike the KKO upper structure, each typology is not necessarily organized according to Peirce’s triadic logic. That is because once we come to organize and classify the real things in the world, we are dealing with objects of a more-or-less uniform character (such as animals or products or atomic elements). There are about 80 such typologies in the KBpedia structure, about 30 of which are deemed “core”, meaning they capture the bulk of the classificatory system. Another document presents these 30 “core” typologies in more detail.
The KKO structure in the figure above is quite different than the first versions of the KKO. As this article series has elaborated, our analysis and then additions of relations to KBpedia has resulted in quite a few changes. These relations, categorized as attributes (1ns), relations (2ns) and representations (3ns) are shown under the 2ns of the Predications branch under Generals. While properties for each of these categories are separately provided under object properties, data properties and annotation properties, they are provided here as class types so that we can reason over these different kinds of relations.
Key Terminology within the Grammar
The complete terminology of the KBpedia ontology is provided through these concepts. However, some of these concepts are more key than others to important structural aspects of the ontology. Thus, besides the universal categories of Firstness, Secondness and Thirdness, here are some of those key concepts, split into three broad groups:
The first group relates to the predicates of the grammar, and includes these three main branches under the Predications node:
- 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, and
- Representations are icons, denotations, 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.
The second broad group are the individual instances within the ontology. Besides the monadic dyads (which are the reifications of the qualities in the ontology), the two main kinds of instances are:
- Events are possibly nameable sequences of time, are described in some manner, can be referenced, and may be related to other time sequences or types, and
- 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 (by count) are the bulk of the overall knowledge base.
The understanding of events from a Peircean viewpoint also leads to a better understanding of actions, activities and processes. Events are a bona fide particular, being an expression of time, while entities, which can have tangible form, are a particular expression of space.
The last grouping relates to the terminology and organization of the Generals branch. Here the key concepts are:
- 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 ).
Understanding the Release Through Its Grammar
When I first adopted this approach of using a speculative grammar, I wrote in part of its advantages :
“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. 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.
“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.”
And then :
“Peirce argues persuasively that how we perceive and communicate things requires this irreducible triadic structure. The symbolic nature of Thirdness means that communication and understanding is a continuous process of refinement, getting us closer to the truth, but never fully achieving it. Thirdness is a social and imprecise mode of communication and discovery, conducted by us and other agents separate from the things and phenomena being observed. Though it is a fallibilistic process, it is one that also lends itself to rigor and methods. The scientific method is a premier example of Thirdness in action.”
We are pleased that our next posting will be the announced release of KBpedia v 150.