Modal Logics for Qualitative Possibility and Beliefs

TL;DR

This paper introduces two modal logics for qualitative reasoning about possibility and necessity, clarifying their relationship with beliefs, conditionals, and possibilistic logic, including connections to Pearl's conditional.

Contribution

It develops two novel modal logics for qualitative possibility and necessity, linking possibilistic logic with belief systems and default reasoning frameworks.

Findings

Identifies relationships between possibilistic logic and beliefs.

Shows that Pearl's conditional aligns with a natural default reasoning conditional.

Provides modal frameworks for qualitative possibility reasoning.

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. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.