Abstract
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 sign-making and its role in the logic of inquiry and truth-testing (semiosis). We begin our analysis of a speculative grammar suitable to knowledge representation with the relevant ‘things’ (nouns) that populate our world and how we organize them. We then expand our discussion of relations to include actions and perceptions (verbs) between these things, as well as how we talk about or describe those things. Peirce’s concept of prescission captures the most fundamental expression of a hierarchical relationship, stated as the relation, prescind. When paired with the lessons of prior chapters, we end up with an expressive grammar for capturing all kinds of internal and external relations to other things. Attributes are the intensional characteristics of an object, event, entity, type (when viewed as an instance), or concept. External relations are actions or assertions between an event, entity, type, or concept and another particular or general. Representations are signs and the means by which we point to, draw attention to, or designate, denote, or describe a particular object, entity, event, type, or general. We now know that attributes are a Firstness in the universal categories; that Secondness captures all events, entities, and relations; and that Thirdness provides the context, meaning, and ways to indicate what we refer to in the world.
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Notes
- 1.
Some material in this chapter was drawn from the author’s prior articles at the AI3:::Adaptive Information blog: “Conceptual and Practical Distinctions in the Attributes Ontology” (Mar. 2015); “KBpedia Relations, Part I: Smarter Knowledge Graphs” (May 2017); “KBpedia Relations, Part II: An Event-Action Model” (May 2017); “KBpedia Relations, Part III: A Three-Relations Model” (May 2017).
- 2.
In OWL 2, “thing” is the root node, with all other vocabulary items being subsidiary to it. Here, we are using “thing” more in keeping with the common vernacular.
- 3.
The role for the label “entity” can also refer to what is known as the root node in some systems such as SUMO. In the OWL language and RDF data model we use, we know the root node as “thing.” Our use of the term “entity” is much different from SUMO and resides at a subsidiary place in the overall TBox hierarchy (see Chap. 8). In this case, and frankly for most semantic matches, equivalences should be judged with care, with context the crucial deciding factor.
- 4.
Though Peirce, as do we, came to believe that Firstness (and Thirdness, for that matter) was real, for something to exist, it must be actual, which is Secondness.
- 5.
They are, however, real, since their type concept exists independent of our thinking about it. Peirce’s insistence that generals may be real helps to situate him among a common split of philosophers into the nominalist, idealist, and realist camps.
- 6.
- 7.
Here, Peirce uses a different sense for reality than his later belief that the universal categories are real. Also, there are many other useful statements by Peirce regarding events; see [5].
- 8.
Within events, we can also categorize according to the three universal categories. The unexpected flash or shock is a Firstness within events. Peirce’s doctrine of tychism places a central emphasis on chance, which he views as the source of processes in nature such as evolution and the “surprising fact” that causes us to reinvestigate our assumptions leading to new knowledge. We more commonly associate an event with action, and that is indeed a major cause of events. (However, chance events or accidents, as an indeterminate group, may trigger events.) An action is a Secondness, however, because it is always paired with a reaction. Reactions may then cause new actions, itself a new event. In this manner activities and processes can come into being, which while combinatorial and compound can also be called events, including those of longer duration. That entire progression of multiple actions represents increasing order, and thus the transition to Thirdness. Peirce makes the interesting insight that thoughts are events, too. “Now the logical comprehension of a thought is usually said to consist of the thoughts contained in it; but thoughts are events, acts of the mind. Two thoughts are two events separated in time, and one cannot literally be contained in the other” (1868, CP 5.288).
- 9.
The most common analogous terms to attributes are properties or characteristics; in the OWL language used by KBpedia, we assign attributes to instances (called individuals) via property (relation) declarations.
- 10.
The act of categorization may thus involve intrinsic factors or external relationships, with the corresponding logics being either intensional or extensional, as discussed further in Chap. 8.
- 11.
J W von Goethe (1749–1832) first explicated the standard three-color scheme. What is more commonly used in design is a four-color scheme from Ewald Hering (1834–1918).
- 12.
Peirce also termed this concept precission, prescisive abstraction, prescision, or precisive abstraction (1902, CP 4.235). It comes from the same root as precision in measurements but has a different meaning as described in the text, which is one reason we prefer the spelling of prescission to distinguish it as much as possible.
- 13.
“Prescind” is often more clearly stated as “prescinded from.” Roughly equivalent phrases are to “leave out of consideration,” “separate from something,” or “withdraw attention from.”
- 14.
There is a very helpful 25-page listing of references dealing with “hierarchy” at the conclusion of Salthe’s 2012 paper, Hierarchical Structures.
- 15.
In the OWL 2 language used by KBpedia, a class is any arbitrary collection of objects. A class may contain any number of instances (called individuals), or a class may be a subclass of another. Instances and subclasses may belong to none, one, or more classes. Both extension and intension may be used to assign instances to classes.
- 16.
In the semantic Web space, “ontology” was the original term because of the interest to capture the nature or being (Greek ὄντως, or ontós) of the knowledge domain at hand. Because the word ‘ontology’ is a bit intimidating, a better variant has proven to be the knowledge graph (because all semantic ontologies take the structural form of a graph). In this book, I tend to use the terms ontology and knowledge graph interchangeably.
- 17.
RDF graphs are more akin to the first sense; OWL 2 graphs more to the latter; see next chapter.
- 18.
I raise the early work by Guarino for a reason. We, the community of KR practitioners, have not gotten our basic grammar right about how we think about these problems. Most everyone still gets bollixed up trying to handle concepts like relations (for me, split into the three categories of attributes, external relations, and representations), events, generals (types or classes), and particulars (individuals or instances). Peircean principles give us logical and defensible ways to think about these problems. That approach strikes me as superior to heated assertions that often lack logical underpinnings.
- 19.
However, we can type attributes, so it is possible to organize and reason over them.
- 20.
At least for Carnap, he thought “… the full meaning of a concept is constituted by two aspects, its intension and its extension. The first part comprises the embedding of a concept in the world of concepts as a whole, i.e., the totality of all relations to other concepts. The second part establishes the referential meaning of the concept, i.e., its counterpart in the real or in a possible world.”
- 21.
See the discussion of semsets in Chap. 10.
- 22.
If validated, they are indeed fact assertions. However, as discussed elsewhere, facts are subject to question and have some degree of fallibility; acceptance of an assertion as fact is a matter of belief.
- 23.
Additional Peirce quotes may be found in my initial article [13].
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Bergman, M.K. (2018). A KR Terminology. In: A Knowledge Representation Practionary. Springer, Cham. https://doi.org/10.1007/978-3-319-98092-8_7
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