Modal logics for qualitative possibility theory

Abstract

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. These logics have a natural semantics based on a qualitative abstraction of possibility distributions. Within this modal framework, we are able to identify interesting relationships among possibilistic logic, beliefs, and conditionals. In particular, we demonstrate that possibilistic logic naturally induces a notion of belief identical to that of the widely used epistemic logic weak S5, and that current approaches to conditional default reasoning and belief revision can be mapped into possibilistic logic, including the means of conditional reasoning based on high probabilities investigated by Adams [1] and Pearl [2, 3].