An Alternative Proof Method for Possibilistic Logic and its Application to Terminological Logics

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be es­ timated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possi­ bility degree or a necessity degree that ex­ presses to what extent the formula is pos­ sibly or necessarily true. Possibilistic reso­ lution yields a calculus for possibilistic logic which respects the semantics developed for possibilistic logic. A drawback, which possibilistic resolution in­ herits from classical resolution, is that it may not terminate if applied to formulas belong­ ing to decidable fragments of first-order log­ ic. Therefore we propose an alternative proof method for possibilistic logic. The main fea­ ture of this method is that it completely ab­ 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 log­ ic. This yields an extension of terminological logics towards the representation of uncer­ tain knowledge which is satisfactory from a semantic as well as algorithmic point of view.