Reasoning in the Description Logic ALC under Category Semantics
Abstract
We present in this paper a reformulation of the usual set-theoretical semantics of the description logic with general TBoxes by using categorical language. In this setting, concepts are represented as objects, concept subsumptions as arrows, and memberships as logical quantifiers over objects and arrows of categories. Such a category-based semantics provides a more modular representation of the semantics of . This feature allows us to define a sublogic of by dropping the interaction between existential and universal restrictions, which would be responsible for an exponential complexity in space. Such a sublogic is undefinable in the usual set-theoretical semantics, We show that this sublogic is {\sc{PSPACE}} by proposing a deterministic algorithm for checking concept satisfiability which runs in polynomial space.
Cite
@article{arxiv.2205.04911,
title = {Reasoning in the Description Logic ALC under Category Semantics},
author = {Ludovic Brieulle and Chan Le Duc and Pascal Vaillant},
journal= {arXiv preprint arXiv:2205.04911},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2110.08837