# Gentzen sequent calculus for possibilistic reasoning

• Churn Jung Liau
• Bertrand I -Peng Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 808)

## Abstract

Possibilistic logic is an important uncertainty reasoning mechanism based on Zadeh's possibility theory and classical logic. Its inference rules are derived from the classical resolution rule by attaching possibility or necessity weights to ordinary clauses. However, since not all possibility-valued formulae can be converted into equivalent possibilistic clauses, these inference 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 ⇒ a kind of modal logic. Then the Gentzen method for modal logics generalized to cover possibilistic logic. Finally, some properties of possibilistic logic, such as Craig's interpolation lemma and Beth's definability theorem are discussed in the context of Gentzen methods.

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