2022/11/11 by Mateusz Urbańczyk, Urbańczyk, Mateusz
Computer Science · #18C20 #18C5 #Category Theory (math.CT) #F.3.2 #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2211.09655
openalex publication_date 2022/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A categorical approach to study model comparison games in terms of comonads was recently initiated by Abramsky et al. In this work, we analyse games that appear naturally in the context of description logics and supplement them with suitable game comonads. More precisely, we consider expressive sublogics of ALCSelfIbO, namely, the logics that extend ALC with any combination of inverses, nominals, safe boolean roles combinations, and Self operator. Our construction augments and modifies the so-called modal comonad by Abramsky and Shah. The approach that we took heavily relies on the use of relative comonads, which we leverage to encapsulate additional capabilities within the bisimulation games in a compositional manner.