Automated Reasoning Using Possibilistic Logic: Semantics, Belief Revision and Variable Certainty Weights

TL;DR

This paper presents a possibilistic logic-based approach to automated deduction under uncertainty, incorporating variable weights, hypothetical reasoning, and non-monotonic inference, with proven completeness and handling of inconsistent knowledge bases.

Contribution

It introduces a novel resolution-based method with variable certainty weights and extends semantics to support incomplete and inconsistent information.

Findings

Proves completeness of the extended resolution principle.

Handles deduction from inconsistent knowledge bases.

Supports hypothetical reasoning with variable weights.

Abstract

In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the refutation method can be generalized. Besides the lower bounds are allowed to be functions of variables involved in the clause, which gives hypothetical reasoning capabilities. The relation between our approach and the idea of minimizing abnormality is briefly discussed. In case where only lower bounds of necessity measures are involved, a semantics is proposed, in which the completeness of the extended resolution principle is proved. Moreover deduction from a partially inconsistent knowledge base can be managed in this approach and displays some form of non-monotonicity.