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Representation Theorems and Locality for Subsumption Testing and Interpolation in the Description Logics εL; εL+ and their Extensions with n-ary Roles and Numerical Domains

Sofronie-Stokkermans V.

Fundamenta Informaticae

2017

Vol. 156, nr 3/4

361--411

In this paper we show that subsumption problems in lightweight description logics (such as εL and εL+) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras, to obtain uniform PTIME decision procedures for CBox subsumption in εL, εL+ and extensions thereof. These locality considerations allow us to present a new family of (possibly many-sorted) logics which extend εL and εL+ with n-ary roles and/or numerical domains. As a by-product, this allows us to show that the algebraic models of εL and εL+ have ground interpolation and thus that εL, εL+, and their extensions studied in this paper have interpolation.