Constructive Satisfiability Procedure for ALCP(Z) (Preliminary Report)

The newly introducedALC(D) extendsALC with path constraints over concrete domainsD. Previous work showed decidability of the satisfiability problem in ALC(D) for various concrete domains, including integer domains. However, the proof of this general result did not provide a complexity upper bound on the problem, or an explicit algorithm for model construction, which is necessary for some reasoning tasks such as abduction. In this paper, we initiate an investigation of the complexity of the satisfiability and model construction problems in ALC(Z), where Z = 〈Z,=, <〉. As a preliminary result towards establishing complexity upper bounds, we present a procedure for deciding satisfiability in a constructive way.