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arXiv:1102.1889cs.LO

Ologs: a categorical framework for knowledge representation

David I. Spivak, Robert E. Kent

Abstract

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

arXiv comments
38 pages
Journal reference
DOI
doi:10.1371/journal.pone.0024274
Subjects
cs.LOLogic in Computer Science cs.AIArtificial Intelligence math.CTCategory Theory

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Linked by 6 identifiable commenters in 7 comments across 7 threads, from May 2017 to Mar 2024.

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Discussed in comments7 threads

  1. SQL is syntactic sugar for relational algebra 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. Modeling Science as a Directed Graph 1 comment

    • Reminds me of ologs: https://arxiv.org/abs/1102.1889v2 The category on top of a given graph just adds path equivalences. While that might not seem like a big addition, it's crucial for restricting the structure's internal state.

      DonbunEf7View on HNParent context

  6. SPARQL Protocol for RDF 1 comment

    • +1 Insightful. In fact, there's research toward showing the two are equivalent in possibility space of what can be represented/queried (https://arxiv.org/abs/1102.1889) But yes, linked data and graphs are super powerful once the data is triplified. Suddenly you have an…

      barakmView on HNParent context

  7. Databases from finite categories 1 comment

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