An alternative proof method for possibilistic logicand its application to terminological logics

  • Authors:
  • Bernhard Hollunder

  • Affiliations:
  • German Research Center for Artificial Intelligence, Saarbrücken, Germany

  • Venue:
  • UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
  • Year:
  • 1994

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Abstract

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree or a necessity degree that expresses to what extent the formula is possibly or necessarily true. Possibilistic resolution yields a calculus for possibilistic logic which respects the semantics developed for possibilistic logic. A drawback, which possibilistic resolution inherits from classical resolution, is that it may not terminate if applied to formulas belonging to decidable fragments of first-order logic. Therefore we propose an alternative proof method for possibilistic logic. The main feature of this method is that it completely stracts from a concrete calculus but uses as basic operation a test for classical entailment. We then instantiate possibilistic logic with a terminological logic, which is a decidable subclass of first-order logic but nevertheless much more expressive than propositional logic. This yields an extension of terminological logics towards the representation of uncertain knowledge which is satisfactory from a semantic as well as algorithmic point of view.