Augmenting concept languages by transitive closure of roles: an alternative to terminological cycles

  • Authors:

  • Franz Baader

  • Affiliations:

  • German Research Center for Artificial Intelligence, Kaiserslautem, Germany

  • Venue:
  • IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
  • Year:
  • 1991

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Abstract

In Baader (1990,1990a), we have considered different types of semantics for terminologicial cycles in the concept language TLQ which allows only conjunction of concepts and value-restrictions. It turned out that greatest fixed-point semantics (gfp-semantics) seems to be most appropriate for cycles in this language. In the present paper we shall show that the concept defining facilities of FLO with cyclic definitions and gfp-semantics can also be obtained in a different way. One may replace cycles by role definitions involving union, composition, and transitive closure of roles. This proposes a way of retaining, in an extended language, the pleasant features of gfp-semantics for FLQ with cyclic definitions without running into the troubles caused by cycles in larger languages. Starting with the language ALC of Schmidt-Schauß&Smolka (1988)--which allows negation, conjunction and disjunction of concepts as well as value-restrictions and exists-in-restrictions--we shall disallow cyclic concept definitions, but instead shall add the possibility of role definitions involving union, composition, and transitive closure of roles. In contrast to other terminological KR-systems which incorporate the transitive closure operator for roles, we shall be able to give a sound and complete algorithm for concept subsumption.