Description logics as polyadic modal logics

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.