Gentzen Sequent Calculus for Possibilistic Reasoning

Possibilistic logic is an important uncertainty reasoning mech anism based on Zadeh s possibility theory and classical logic The deduc tion rules of possibilistic logic have been obtained from classical resolu tion rule by attaching possibility or necessity weight to ordinary clauses However since not all possibility valued formulae can be converted into equivalent possibilistic clauses the resolution rules are somewhat re stricted In this paper we develop Gentzen sequent calculus for possi bilistic reasoning to lift this restriction This is done by rst formulating possibilistic reasoning as a kind of modal logic Then the Gentzen method for modal logics are generalized to it Finally some properties of possi bilistic logic such as Craig s interpolation lemma and Beth s de nability theorem are also discussed in the context of Gentzen methods