A UML-based method for deciding finite satisfiability in description logics

Finite satisfiability in Description Logics and in UML class diagrams is the problem of deciding whether a concept (a class) has a finite, non-empty extension in some model. The problem is known to be hard. Standard DL reasoners do not reason about finite satisfiability. In this article we introduce class diagram translations for major operators in description logics, and extend a previous UML finite satisfiability decision algorithm to handle these translations. The contribution of this article is in presenting an efficient method for deciding finite satisfiability in atomic, primitive knowledge bases of popular description logics, using a translation to UML class diagrams. The method applies to class hierarchies that do not include cycles with disjoint or complete constraints. The scope can be determined in a preprocessing step. The suggested method is valuable since standard DL reasoners do not reason about finite satisfiability,.