Modal Logics for Qualitative Possibility and Beliefs
This work addresses foundational issues in AI and logic for researchers interested in uncertainty reasoning, but it is incremental as it builds on existing possibilistic and modal frameworks.
The paper tackles the problem of developing qualitative accounts of possibility and necessity by presenting two modal logics for representing and reasoning with such statements, and it identifies relationships between possibilistic logic, beliefs, and conditionals, showing that a natural conditional for default reasoning matches Pearl's conditional for e-semantics.
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.