Using tableau to decide description logics with full role negation and identity

Abstract

This article presents a tableau approach for deciding expressive description logics with full role negation and role identity. We consider the description logic ALBO id , which is ALC extended with the Boolean role operators, inverse of roles, the identity role, and includes full support for individuals and singleton concepts. ALBO id is expressively equivalent to the two-variable fragment of first-order logic with equality and subsumes Boolean modal logic. In this article, we define a sound, complete, and terminating tableau calculus for ALBO id that provides the basis for decision procedures for this logic and all its sublogics. An important novelty of our approach is the use of a generic unrestricted blocking mechanism. Unrestricted blocking is based on equality reasoning and a conceptually simple rule, which performs case distinctions over the identity of individuals. The blocking mechanism ties the proof of termination of tableau derivations to the finite model property of ALBO id .