Locality and subsumption testing in EL and some of its extensions

In this paper we show that subsumption problems in many lightweight description logics (including EL and EL+) 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 EL and extensions thereof. These locality considerations allow us to present a new family of (possibly many-sorted) logics which extend EL and EL+ with n-ary roles and/or numerical domains.