A Logic of Graded Possibility and Certainty Coping with Partial Inconsistency

TL;DR

This paper introduces a semantics for possibilistic logic using fuzzy sets of interpretations, allowing reasoning with weighted formulas and handling partial inconsistency effectively.

Contribution

It proposes a new semantics based on fuzzy interpretations for possibilistic logic, extending satisfiability to fuzzy sets and proving soundness and completeness of a generalized resolution method.

Findings

Semantics based on fuzzy sets accommodates partial inconsistency.

Automated deduction via generalized resolution is sound and complete.

Possibilistic knowledge bases are represented as sets of possibility distributions.

Abstract

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency.