Completing the Schema for the Relations Addition

In the previous part of this series I discussed the relations model that we are adding to the KBpedia knowledge structure for its upcoming version 1.50. This article continues that discussion by fleshing out the concept hierarchy for this relations addition. These changes are taking place within the upper structure of KBpedia, what we call the KBpedia Knowledge Ontology, or KKO. The addition of this relations model affects both the class hierarchy of KKO and its properties structure. Both aspects are discussed below.

The previous parts of this series introducing the new KBpedia v 150 provide the rationale for adding a relations or predications structure to KBpedia, as well as the rationale for grounding this structure in the universal categories and logic of relations developed by Charles Sanders Peirce. Let me expand on those arguments a bit further here.

Recall from the earlier parts in this discussion that we want to adopt a schema for relations because we are interested in assertions and propositions in our knowledge structures. As Peirce notes [1],”The unity to which the understanding reduces impressions is the unity of a proposition. This unity consists in the connection of the predicate with the subject; and, therefore, that which is implied in the copula, or the conception of being, is that which completes the work of conceptions of reducing the manifold to unity.” (CP 1.548). The previous part discussed the rationale for three main classes of relationship types and how they related to Peirce’s views on logic and the theory of signs (semiosis). It is now time to expand on those distinctions.

The Second Level of the Relations Hierarchy

At the top level, relations are defined in KBpedia as belonging to one of three main types: Attributes, which are how we describe and characterize individual things (using the shorthand of A:A); External Relations, which are how an individual thing may relate, interact or situate with regard to external things (using the shorthand of A:B); or Representations [3], which are how we may name or define, indicate or reference, or provide supporting information about an individual thing (using the shorthand of re:A). These three main categories capture every conceivable form of relation. Note that an individual thing may also include classes or types, as well as individuals. Through this means, we can talk about and refer to categories, concepts, classes or types when we need to consider them as things unto themselves.

These three main categories correspond to Peirce’s universal categories of Firstness, Secondness and Thirdness [2]. (Where appropriate, I also sometimes footnote some Peirce quotes relevant to the category at hand.) Using the same trichotomous approach to categorization [2], we can now expand these three main relational categories into a second level of nine categories:

For Attributes (A:A), the split is into these three categories:

• Intrinsic — innate characteristics or essences of single entities or events (particulars). Example concepts include oneness, qualities, feelings, inherent, negation, is, has, intensional, naturalness, internal, innateness
• Adjunctual — events that may occur to a single entities or events (particulars) that help characterize it. Example concepts include birth, death, marriage, events, accidents, surprises, happenings, extrinsic, adjunctual
• Contextual — circumstances or placements of single entities or events (particulars) that help characterize it. Example concepts include space, time, continuity, contiguous, smooth, otherness, ratings, level, situational (w/ respect to A), sensible, contiguous, all placements thereto, derivative, classificatory, rankings.

For External Relations (A:B), the split is into these three categories:

• Direct — a simple, direct relationship (no intermediaries) between two different objects (entities, events, or their types, considered as instances). Example concepts include is a, simple without parts, part of, members in types or classes, genealogical roles (parent, child, brother), identity, extensional
• Copulative — relationships of combination, membership, quantity, action, or circumstance. Example concepts include accidental, real, place, time, situation, quantity, facets, aspects, conjunctive, one-to-many, many-to-one, sum of, contextual, verbs
• Mediative — true, triadic external relations, such as “A gives B to C”; relationships of relevance, meaning or explanation – namely, thirdness – about subjects and types. Example concepts include concepts, generalities, similarity, genres, aspects, comparison, performance, thought, triadic, agreement/difference, placement in space/time (contiguity), conditional, reasoning, classification.

And, for Representations (re:A), the split is into these three categories:

• Denotatives — icons or symbols that name or describe the subject. Example concepts include names, labels, images, descriptions, definitions, denotations, icons, designations, proper nouns
• Indexes — indirect references or pointers that help situate or draw attention to the subject. Example concepts include URIs, identifiers, keys, indices, references, semes, propositions (w/o objects), codes, selections, directional, citations, pronouns [4]
• Associatives — a situational and contextual assertion of proximity, affiliation or adjacency of the subject with regard to any contiguity. Example concepts include see also, lists, links (incoming + outgoing), associations, likenesses, resemblances [5].

The Third Level of the Relations Hierarchy

For the next level, we can continue with our process of categorization based on the universal categories applied to the nine categories listed above. Here is the schema that results from this approach:

For the mid-level category of Intrinsics, the first of three categories under Attributes, here are the three subsidiary categorizations (representing the Firstness, Secondness and Thirdness, respectively):

• Qualities — an internal characteristic or aspect of an object; collectively these define intensionally what kind of thing to which the object belongs, though that relationship is not intrinsic
• Elementals — a contributing part of or integral input or aspect that adds to the understanding about the subject (A)
• Configurations (forms) — forms or arrangements that are of the nature or perceivable of the subject (A).

For the mid-level category of Adjunctual, here are the three subsidiary categorizations:

• Quantities — a characteristic of a subject (A) that is expressed as a number quantity
• Eventuals — chance, accidental or planned occurrences that directly involve subject (A)
• Extrinsics — external events or circumstances that directly involve subject (A) or help define the nature or reality of subject (A).

For the mid-level category of Contextual, here are the three subsidiary categorizations:

• Situants — attributes or characteristics that help situate, or place in a locational context, the subject (A)
• Ratings — an assigned value or characterization that orders subject (A) in relation to other subjects for a given attribute
• Classifications — a characterization of subject (A) that involves evaluating subject (A) and providing a multi-factor typing, coding or value in relation to a given attribute or set of attributes.

For the mid-level category of Direct, the first of three categories under External Relations, here are the three subsidiary categorizations:

• Equivalences — a simple, direct relatiionship between a subject (A) and an object (B) that asserts equalness or sameness
• Parts — a simple, direct relationship where the object (B) is a part of or component of subject (A), including the idea of ‘whole’
• Descendants — a simple, direct relationship where object (B) is a direct child or parent or subsumption (hyponym) or supersumption (hypernym) to subject (A).

For the mid-level category of Copulative, here are the three subsidiary categorizations:

• Typings (is B) — this simple relation is for all of the is-a relations to types (B) for subject (A). Identities and common names fit into this category
• ActionTypes — simple relations of energetics, perception or thought of subject (A) to some other object (B)
• Conjoins — relations that involve the joining of a subject (A) to an object (B) via an intermediate object.

For the mid-level category of Mediative, here are the three subsidiary categorizations:

• Comparisons — relations that compare, contrast or size up similarities or differences or overlaps between subject (A) and object (B)
• Performances — relations of quantity or rank for how subject (A) performed in relation to object (B)
• Circumstances — relations of subject (A) to external circumstances, situations or contexts.

For the mid-level category of Denotatives, the first of three categories under Representations, here are the three subsidiary categorizations:

• Media — iconic images or sounds that invoke the identification with a given object or representation. Media in this sense draws attention to the object [6]
• Labels — symbolic text strings that help to name or draw attention to a particular object
• Descriptions — text strings that may be longer than labels and provide additional or contextual information or specify attributes about the object, beyond drawing attention.

For the mid-level category of Indexes, here are the three subsidiary categorizations:

• Pointers — physical or symbolic indicators of a given thing and which draw attention to it
• Identifiers — generally (unique) symbols or strings that provide a key to the given subject, often within some conventional scheme for generating and recognizing the token assigned
• Codes — an assigned symbolic token or string that groups the object with similar items; the generation and interpretation of the token is (often) done in relation to an understood schema. Indexes are included in this category.

And, lastly, for the mid-level category of Associatives, here are the three subsidiary categorizations:

• Lists — an aggregation, either ordered or unordered, of objects similar to one another with respect to given characters or types
• Relateds (see also) — an indicator of some nature to other objects similar or related to the given object; the criteria and degree or strength of relationship between the items are indeterminate
• Augments — an indicator to an external factor in relation to the object, which factor itself leads to still further explanations.

These categories, then, complete the three levels underneath the KBpedia Knowledge Ontology’s Predications branch (itself a Secondness under the basic Thirdness of Generals). We have established these as concepts within KKO such that we may reason over the ideas of these categories, and do other conceptual work with them. This conceptualization is helpful in order to consider the ideas of predicates and the relationships between them. However, for mapping properties from external sources, we need a parallel structure in terms of KKO properties.

An Analogous Structure for Properties

We thus created an analogous structure for properties within KBpedia. One useful addition that is forthcoming in the KBpedia v 1.50 release is a mapping of 2500 Wikidata properties to this property schema, which represents more than 95% of all property assignments to the 25 million+ entities within Wikidata. This is one of the first tangible expressions of the benefits of having a fully rational predicate structure within KBpedia.

Attributes, External Relations and Representations comprise OWL properties. In general, Attributes correspond to the OWL datatypes property; External Relations to the OWL object property; and Representations to the OWL annotation properties. These specific OWL terms are not used in our KKO 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 KKO’s grammar to existing OWL properties is quite close. In all cases, our mappings to external sources are done via the subPropertyOf relation in OWL.

Object and Data Properties

Because a given external non-annotation property (that is, all properties except Representations) may either refer to another object (IRI) or to a string or data value, we created parallel listings of object and datatype properties within KKO. Here is the listing for the object properties group as shown by a screen capture from Protégé:

Note that Protégé lists its items alphabetically, rather than our preferred ordering of Firstness, Secondness and Thirdness. You also should note the parallelism to the concept hierarchy discussed above. Not shown is the similar datatype properties structure.

Annotation Properties

As noted, Representations correspond to annotation properties, and that listing is shown in this screen capture:

In OWL2, annotations may be organized in a subPropertyOf manner, even though inferencing is not possible over this structure. The organization, though, is helpful to understand relationships (and they can independently be reasoned over with the matching concept structure) and may be used in search, SPARQL or external analytic scripts.

We also organize the SKOS and Dublin Core annotation properties used by KKO into the categorical structure of these Representations, as shown by the screen capture above. This organization helps elucidate the structure under the Representations branch using these commonly applied properties.

Some Caveats and Next Part

This completes the hierarchical specification of the Predications branch within KKO. These 39 categories (3 + 9 + 27), following the categorization approach suggested by Peirce’s universal categories, now complete our additions to this next version of KBpedia.

This addition has been under intense and active development for the past year, though it has been in the works for much longer than that. Over that time, the names of categories and, indeed, even the splits themselves, have changed frequently and evolved. Peirce’s Logic of Relatives [7], as one of the two main sources, is itself laid out in a dichotomous structure, though elsewhere in Peirce’s writings — as we showed in the previous parts — these are often expressed in Peirce’s more standard trichotomous structure. I am sure with use and more experience that we will see further refinements to the KBpedia relations schema as time goes on. Please do not be surprised if you see further changes.

We are now nearly complete with the advance material leading up the KBpedia v 1.50 release. We will have one next part in our series recapitulating the terminology and grammar for this new version. The announcement following that will finally release version 1.50.

Attributes, External Relations and Representations Form the Trichotomy

The forthcoming release of KBpedia version 1.50 deals primarily with the addition of a relations schema to the knowledge structure. In the previous part of this series, I discussed the event-action model at the heart of the schema. Actions are external relations between two objects, including parts, for which we use the variable shorthand of A and B. In terms of the universal categories of Charles Sanders Peirce [1], these dyadic relations are a Secondness that we formally term External Relations, or A:B.

But external relations do not constitute the complete family of relations. External relations are but one form of predicate we require. We need relations that cover the full range of language usage, as well as the entire scope of OWL properties. KBpedia is written in OWL2, which is the semantic ontology language extension of RDF. We need to capture the three types of properties in OWL2, namely object properties, datatype properties, and annotation properties.

In Peircean terms, we thus need relations that characterize the subject itself (A:A), which are mostly datatype properties, as well as statements about the subject (re:A), which are annotation properties. Most external relations are represented by object properties in OWL2, but sometimes datatype properties are also used [2].

We call relations of subject characterizations Attributes, and these are a Firstness within Peirce’s universal categories. We call relations about the subject Representations, and these are a Thirdness within the universal categories. The purpose of this part in our series is to introduce and define these three main branches of relations — Attributes, External Relations, and Representations — within the KBpedia schema.

Nature of the Trichotomy

In accordance with the design basis of KBpedia, we use Peirce’s universal categories and his writings on logic and semiosis (signs) to provide the intellectual coherence for the design. For the analysis of relations, two additional Peirce manuscripts were closely studied. The first manuscript is the first one on logic relations by Peirce in 1870, which goes by the shorthand of DNLR [3]. The second manuscript was from nearly 20 years later, known simply as the “Logic of Relatives” [4]. These two manuscripts deal with the ideas of internal and external relations, or the Attributes and External Relations, respectively, discussed above, and relate more to the predicate side of propositions. However, we also need to reference or point to the subjects of the proposition and to predicates, for which the Representations portion applies. Our need here was to organize a full breadth of relations in context with the universal categories, the needs of knowledge representation, and the structure of properties within OWL2 [5]. The result, we think, is consistent with the Peircean architectonic, but modernized for KR purposes.

For example, Peirce notes “the law of logic governs the relations of different predicates of one subject” (CP 1.485). In expanding on this law he states:

“Now logical terms are of three grand classes.

“The first embraces those whose logical form involves only the conception of quality, and which therefore represent a thing simply as “a ──”. These discriminate objects in the most rudimentary way, which does not involve any consciousness of discrimination. They regard an object as it is in itself as such (quale); for example, as horse, tree, or man. These are absolute terms.

“The second class embraces terms whose logical form involves the conception of relation, and which require the addition of another term to complete the denotation. These discriminate objects with a distinct consciousness of discrimination. They regard an object as over against another, that is as relative; as father of, lover of, or servant of. These are simple relative terms.

“The third class embraces terms whose logical form involves the conception of bringing things into relation, and which require the addition of more than one term to complete the denotation. They discriminate not only with consciousness of discrimination, but with consciousness of its origin. They regard an object as medium or third between two others, that is as conjugative; as giver of ── to ──, or buyer of ── for ── from ──. These may be termed conjugative terms.

“The conjugative term involves the conception of third, the relative that of second or other, the absolute term simply considers an object. No fourth class of terms exists involving the conception of fourth, because when that of third is introduced, since it involves the conception of bringing objects into relation, all higher numbers are given at once, inasmuch as the conception of bringing objects into relation is independent of the number of members of the relationship. Whether this reason for the fact that there is no fourth class of terms fundamentally different from the third is satisfactory of not, the fact itself is made perfectly evident by the study of the logic of relatives.” (CP 3.63) [1]

We take the first “class” above as largely relating to the Attributes. The next two classes, including the conjugative terms, we relate to External Relations. To this we add the Representations as the Thirdness within our revised relations category. Each of these three categories is described more fully below with further discussion as to the rationale for these splits.

We think this organization of relational categories is consistent with Peirce’s thinking, even though he never had today’s concepts of computerized knowledge representation as an objective for his analysis. For example, he labeled one of his major sections “The Conceptions of Quality, Relation and Representation, Applied to this Subject.” (1867, “Upon Logical Comprehension and Extension”; CP 2.418) Thirty five years later, Peirce still held to this split,”. . . there are but three elementary forms of predication or signification, which as I originally named them (but with bracketed additions now made to render the terms more intelligible) were qualities (of feeling), (dyadic) relations, and (predications of) representations.” (1903, EP 424; CP 1.561)

And, of course, human intelligence and communication is a symbolic world. So, our computer-reasoning basis should also be geared to the manipulation of ideas, which in a knowledge context is the accumulation of (approximately) known false and known true assertions about the world. These are our statements or propositions or assertions. Peirce elaborates:

“Now every simple idea is composed of one of three classes; and a compound idea is in most cases predominantly of one of those classes. Namely, it may, in the first place, be a quality of feeling, which is positively such as it is, and is indescribable; which attaches to one object regardless of every other; and which is sui generis and incapable, in its own being, of comparison with any other feeling, because in comparisons it is representations of feelings and not the very feelings themselves that are compared [Attributes]. Or, in the second place, the idea may be that of a single happening or fact, which is attached at once to two objects, as an experience, for example, is attached to the experiencer and to the object experienced [External Relations]. Or, in the third place, it is the idea of a sign or communication conveyed by one person to another (or to himself at a later time) in regard to a certain object well known to both [Representations].” (CP 5.7) (Emphasis brackets added.)

Peirce’s recommendations as to how to analyze a question proceed from defining the domain and its relations (the speculative grammar) to the logical analysis of it, including hypotheses about still questionable areas or emerging from new insights or combinations. The methods of this progression should be purposeful and targeted to produce a better likelihood of economic results or outcomes. This overall process he called the pragmatic maxim, and is a key insight into Peirce’s reputation at the father of pragmatism.

The concepts above, then, represent our starting speculative grammar for how to organize the relations, including the choice of the three adics, or branches of the trichotomy [6]. We also set the guidance of how each adic branch may be analyzed and split according to the universal categories (which is the subject of the next Part IV in this series.)

Nature of Propositions and Predicates

In terms of Peirce’s more formal definition of signs, a proposition is a dicisign, and it consists of a subject + predicate. (CP 2.316) A predicate is a rhema (CP 2.95). In terms of OWL2 with its RDF triples (subject – property – object), the predicate in this model is property + object, or a multitude of annotations that are representations of the subject. Further, “Every proposition refers to some index” (CP 2.369), that is its subject (also referred to as object). “Thus every kind of proposition is either meaningless or has a real Secondness as its object.” (CP 2.315) The idea of an individual type (or general) is also a Secondness [7]. “I term those occasions or objects which are denoted by the indices the subjects of the assertion.” (CP 2.238) The assertion give us the basic OWL statement, also known as a triple.

A proposition captures a relation, which is the basis for the assertion about the ‘subjects’. “Any portion of a proposition expressing ideas but requiring something to be attached to it in order to complete the sense, is in a general way relational. But it is only a relative in case the attachment of indexical signs will suffice to make it a proposition, or, at least, a complete general name.” (CP 3.463)  “But the Logic of Relations has now reduced logic to order, and it is seen that a proposition may have any number of subjects but can have but one predicate which is invariably general.” (CP 5.151)

We now have the building blocks to represent the nature of the proposition:

Subject(s) and a general predicate make up the proposition (statement, assertion). Subjects need to be individual things (including generals) and are defined, denoted and indicated by various indexical representations, including icons and images. Active predicates that may be reasoned over include the attributes (characteristics) of individual subjects or the relations between objects.

This basic structure also lends itself to information theoretics. “Every term has two powers or significations, according as it is subject or predicate. The former, which will here be termed its breadth, comprises the objects to which it is applied; while the latter, which will here be termed its depth, comprises the characters which are attributed to every one of the objects to which it can be applied.” (CP 2.473) Peirce importantly defines the total information regarding a subject to consist of the “sum of synthetical propositions in which the symbol is subject or predicate, or the information concerning the symbol.” (CP 2.418) In other words, information = breadth x depth. We can reason over attributes and external relations, but our total information also consists in our representations.

These insights give us some powerful bases for defining and categorizing the terms or tokens within our knowledge space. By following these constructs, I believe we can extract the maximum information from our input content.

Definitions of the Relations

Best practice using semantic technologies includes providing precise, actionable definitions to key concepts and constructs. Here are the official statements regarding this trichotomy of relations.

Attribute Relations

Attributes are the intensional characteristics of an object, event, entity, type (when viewed as an instance), or concept. The relationship is between the individual instance (or Particular) and its own attributes and characteristics, in the form of A:A. Attributes may be intrinsic characteristics or essences of single particulars, such as colors, shapes, sizes, or other descriptive characteristics. Attributes may be adjunctual or accidental happenings to the particular, such as birth or death. Or, attributes may be contextual in terms of placing the particular within time or space or in relation to external circumstances.

Attributes are specific to the individual, and only include events that are notable for the individual. They are a Firstness, and in totality try to capture the complete characteristics of the individual particular, which is a Secondness.

These attributes are categorized according to these distinctions and grouped and organized into types, which will be presented in the next part.

External Relations

External relations are assertions between an object, event, entity, type, or concept and another particular or general. An external relationship has the form of A:B. External relations may be simple ones of a direct relationship between two different instances. External relations may be copulative by combining objects or asserting membership, quantity, action or circumstance. Or, external relations may be mediative to provide meaning, context, relevance, generalizations, or other explanations of the subject with respect to the external world. External relations are extensional.

External relations are by definition a Secondness. These external relations are categorized according to these distinctions and grouped and organized into types, which will be presented in the next part.

The events discussion in the previous Part II pertained mostly to external relations.

Representational Relations

Representations are signs (CP 8.191), and the means by which we point to, draw or direct attention to, or designate, denote or describe a particular object, entity, event, type or general.  A representational relationship has the form of re:A. Representations can be designative of the subject, that is, be icons or symbols (including labels, definitions, and descriptions). Representations may be indexes that more-or-less help situate or provide traceable reference to the subject. Or, representations may be associations, resemblances and likelihoods in relation to the subject, more often of indeterminate character.

The representational relation includes what is known as annotations or metadata in other contexts, such as images, links, labels, descriptions, pointers, references, or indexes. Representations can not be reasoned over, except abductive reasoning, but some characteristics may be derived or analyzed through non-inferential means.

These representations are categorized according to these distinctions and grouped and organized into types, which will be presented in the next part.

Summary of the Three Relations

We can now pull these threads together to present a summary chart of these three main relational branches:

This trichotomy sets the boundaries and affirms the method by which further sub-divisions will be presented in the next installment in this series.

A Strong Relation Schema

We now have a much clearer way for how to build up the assertions in our knowledge representations, according to linguistic predicate construction and predicate calculus. We can now explicitly state a premise underlying our choice of Peirce and his architectonic for the design of KBpedia: it is the most accurate, expressive basis for capturing human language and logical reasoning, both individually and together. Our ability to create new symbolic intelligence from human knowledge requires that we be able to compute and reason over human language.

In the next part we will establish sub-categories for each of these three branches according to the universal categories [8].