Affiliation:
1. University of Manchester, Manchester, U.K
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
.
Funder
Engineering and Physical Sciences Research Council
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
9 articles.
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