publication . Preprint . 2017

Knowledge Representation in Bicategories of Relations

Patterson, Evan;
Open Access English
  • Published: 01 Jun 2017
Abstract
We introduce the relational ontology log, or relational olog, a knowledge representation system based on the category of sets and relations. It is inspired by Spivak and Kent's olog, a recent categorical framework for knowledge representation. Relational ologs interpolate between ologs and description logic, the dominant formalism for knowledge representation today. In this paper, we investigate relational ologs both for their own sake and to gain insight into the relationship between the algebraic and logical approaches to knowledge representation. On a practical level, we show by example that relational ologs have a friendly and intuitive--yet fully precise--g...
Subjects
free text keywords: Computer Science - Artificial Intelligence, Computer Science - Logic in Computer Science, Mathematics - Category Theory
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ΔA := [x : A, y : A × A | hx, xi = y] A := [x : A, y : 1 | >]

HA := [x : A + A, y : A | δ (x, x1 : A.x1, x2 : A.x2) = y]

Abstract
We introduce the relational ontology log, or relational olog, a knowledge representation system based on the category of sets and relations. It is inspired by Spivak and Kent's olog, a recent categorical framework for knowledge representation. Relational ologs interpolate between ologs and description logic, the dominant formalism for knowledge representation today. In this paper, we investigate relational ologs both for their own sake and to gain insight into the relationship between the algebraic and logical approaches to knowledge representation. On a practical level, we show by example that relational ologs have a friendly and intuitive--yet fully precise--g...
Subjects
free text keywords: Computer Science - Artificial Intelligence, Computer Science - Logic in Computer Science, Mathematics - Category Theory
Download from

ΔA := [x : A, y : A × A | hx, xi = y] A := [x : A, y : 1 | >]

HA := [x : A + A, y : A | δ (x, x1 : A.x1, x2 : A.x2) = y]

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