Gentzen Sequent Calculus for Possibilistic Reasoning

. Possibilistic logic is an important uncertainty reasoning mechanism based on Zadeh's possibility theory and classical logic. The deduction rules of possibilistic logic have been obtained from classical resolution 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 restricted. In this paper, we develop Gentzen sequent calculus for possibilistic reasoning to lift this restriction. This is done by first formulating possibilistic reasoning as a kind of modal logic. Then the Gentzen method for modal logics are generalized to it. Finally, some properties of possibilistic logic, such as Craig's interpolation lemma and Beth's definability theorem are also discussed in the context of Gentzen methods. 1 Introduction Recently, many uncertainty reasoning mechanisms based on Zadeh's possibility theory[14] have grown rapidly. (See [4] for ..

Gentzen sequent calculus for possibilistic reasoning

Abstract. Possibilistic logic is an important uncertainty reasoning mechanism based on Zadeh's possibility theory and classical logic. The deduction rules of possibilistic logic have been obtained from classical resolution 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 restricted. In this paper, we develop Gentzen sequent calculus for possibilistic 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 possibilistic logic, such as Craig's interpolation lemma and Beth's de nability theorem are also discussed in the context of Gentzen methods.