Description logics as polyadic modal logics

TL;DR

This paper explores extending description logics into polyadic modal logics using relation algebras, exemplified by a polyadic ALC with permutation and counting, emphasizing conceptual insights.

Contribution

It introduces a novel framework for polyadic description logics via relation algebras, expanding the expressiveness of standard description logics.

Findings

Develops a general relation algebra framework for polyadic modal logics

Introduces a polyadic version of ALC with permutation and counting operators

Focuses on conceptual foundations rather than technical details

Abstract

We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a concrete system to illustrate our approach, we investigate the polyadic version of ALC extended with relational permutation operators and tuple counting. The focus of the paper is conceptual rather than technical.