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

  • Authors:

  • Guilin Qi;Jeff Z. Pan

  • Affiliations:

  • Institute AIFB, University of Karlsruhe, Germany;Department of Computing Science, The University of Aberdeen,

  • Venue:
  • ASWC '08 Proceedings of the 3rd Asian Semantic Web Conference on The Semantic Web
  • Year:
  • 2008

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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.