2021/10/17 by Chan Le Duc, Duc, Chan Le · 1 citation
Computer Science · #Semantic Web and Ontologies #Logic, Reasoning, and Knowledge #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.2110.08837
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.