A Tableau Algorithm for Possibilistic Description Logic $\mathcal{ALC}$

Abstract

Uncertainty reasoning and inconsistency handling are two important problems that often occur in the applications of the Semantic Web. Possibilistic description logics provide a flexible framework for representing and reasoning with ontologies where uncertain and/or inconsistent information is available. Although possibilistic logic has become a popular logical framework for uncertainty reasoning and inconsistency handling, its role in the Semantic Web is underestimated. One of the challenging problems is to provide a practical algorithm for reasoning in possibilistic description logics. In this paper, we propose a tableau algorithm for possibilistic description logic $\mathcal{ALC}$ . We show how inference services in possibilistic $\mathcal{ALC}$ can be reduced to the problem of computing the inconsistency degree of the knowledge base. We then give tableau expansion rules for computing the inconsistency degree of a possibilistic $\mathcal{ALC}$ knowledge. We show that our algorithm is sound and complete. The computational complexity of our algorithm is analyzed. Since our tableau algorithm is an extension of a tableau algorithm for $\mathcal{ALC}$ , we can reuse many optimization techniques for tableau algorithms of $\mathcal{ALC}$ to improve the performance of our algorithm so that it can be applied in practice.