Reasoning about higher order uncertainty in possibilistic logic

Abstract

Possibilistic logic is an important approach for reasoning about possibility and necessity. By formulating possibilistic reasoning as a kind of modal logic, we can represent and reason about higher order uncertainty to any nested degrees. In this paper, we present a system with built-in axioms for reasoning about higher order uncertainty. Some intuition behind the system is discussed and the soundness and completness of it with respect to the class of finite transitive and serial (in fuzzy set-theoretic sense) possible-world models are proved.