Category-theoretical Semantics of the Description Logic ALC (extended version)
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Abstract (arXiv)
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this paper a reformulation of the usual set-theoretical semantics of the description logic ALC by using categorical language. In this setting, ALC concepts are represented as objects, concept subsumptions as arrows, and memberships as logical quantifiers over objects and arrows of categories. Such a category-theoretical semantics provides a more modular representation of the semantics of ALC and a new way to design algorithms for reasoning.
Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Oct 2021.
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Citing papers per year: 2022: 1; 2023: 1; 2024: 0; 2025: 1; 2026: 1.
4 papers.
- 2022Reasoning in the Description Logic ALC under Category Semanticscited by 3
- 2025A New Tractable Description Logic under Categorical Semanticscited by 1
- 2023Lattice-preserving ALC ontology embeddings with saturationcited by 0
- 2026TAPO-Description Logic for Information Behavior: Refined OBoxes, Inference, and Categorical Semanticscited by 0
- 2026TAPO-Description Logic for Information Behavior: Refined OBoxes, Inference, and Categorical Semantics23 Apr 2026
- 2025A New Tractable Description Logic under Categorical Semantics13 May 2025
- 2023Lattice-preserving ALC ontology embeddings with saturation11 May 2023
- 2022Reasoning in the Description Logic ALC under Category Semantics10 May 2022