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arXiv · 2205.04911

Reasoning in the Description Logic ALC under Category Semantics

Ludovic Brieulle·Chan Le Duc·Pascal Vaillant
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Abstract

We present in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ with general TBoxes by using categorical language. In this setting, $\mathcal{ALC}$ 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 $\mathcal{ALC}$. This feature allows us to define a sublogic of $\mathcal{ALC}$ 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.

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Ludovic Brieulle, Chan Le Duc, Pascal Vaillant. 2022-05-10. Reasoning in the Description Logic ALC under Category Semantics. https://arxiv.org/abs/2205.04911

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