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arXiv:1706.00526cs.AI

Knowledge Representation in Bicategories of Relations

Evan Patterson

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--graphical syntax, derived from the string diagrams of monoidal categories. We explain several other useful features of relational ologs not possessed by most description logics, such as a type system and a rich, flexible notion of instance data. In a more theoretical vein, we draw on categorical logic to show how relational ologs can be translated to and from logical theories in a fragment of first-order logic. Although we make extensive use of categorical language, this paper is designed to be self-contained and has considerable expository content. The only prerequisites are knowledge of first-order logic and the rudiments of category theory.

arXiv comments
Journal reference
DOI
Subjects
cs.AIArtificial Intelligence cs.LOLogic in Computer Science math.CTCategory Theory

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Linked by 5 identifiable commenters in 7 comments across 7 threads, from Jun 2017 to Feb 2020.

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Discussed in comments7 threads

  1. Contextualise: Manage your knowledge 1 comment
  2. Software Architecture Guide 1 comment

    • Haskell is not really category-theoretic. The category Hask doesn't quite line up with real-world Haskell. The disconnection is well-understood and well-documented [0][1]. Category theory can directly give us systems from theories. See the papers behind FQL/CQL for more details…

      lidHanteykView on HNParent context

  3. A Formal Apology for Metaphysics [pdf] 1 comment

    • Mathematics is metaphysics. I'd like your refutation to center on any nuance which might separate the two disciplines other than the sad fact that many philosophers don't learn much maths. Logic is metaphysics: https://philpapers.org/archive/ALVLIM-3.pdf Logic is mathematical…

      myWindoonnView on HNParent context

  4. Kialo – a platform for rational debate 1 comment

    • Unfortunately, Kialo does not have any features for structural reasoning, where the logical connections between arguments are completely formalized and precise. It relies on a human element to check each argument. Edit: How to do this formally? Look at formal systems for hints…

      myWindoonnView on HNParent context

  5. The Logical Disaster of Null 1 comment

    • You seem intelligent, so I'm going to drop you into the deep end. In category theory, a topos [0][1] (plural topoi) is a structure-place where logic can be done. Boolean logic corresponds to a particular topos. Actually, there are at least two topoi which do Boolean logic; one…

      DonbunEf7View on HNParent context

  6. Modeling Science as a Directed Graph 1 comment

    • Thanks. In a similar vein, there's a recent Knowledge Representation in Bicategories of Relations https://arxiv.org/pdf/1706.00526.pdf .

      mncharityView on HNParent context

  7. A computational linguistic farce in three acts 1 comment

    • Recently Coecke comments on Gärdenfors geometric meaning in the context of his categorical semantics that I'm finding interesting, in arXiv:1608.01402. What I would welcome is a computational link relating that semantics and oldie semantic-network based ideas. For instance in…

      jesuslopView on HNParent context

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