Abstract
Concept languages are languages allowing one to express general properties of classes of objects and their mutual relationships. They originated from the ideas developed for frame-based systems and semantic-networks, especially the KL-ONE system. We consider a concept language called ALUNI, comprising unions of concepts, number restrictions and inverse roles, and address the problems of both finite satisfiability and finite implication in a knowledge base constituted by a finite set of inclusion statements which express relevant properties of ALUNI concepts. Decidability of both problems is shown by introducing a novel technique based on linear programming and that has never been studied before in the context of concept languages.