Revising possibilistic knowledge bases via compatibility degrees

Abstract

Possibilistic logic is a weighted logic for dealing with incomplete and uncertain information by assigning weights to propositional formulas. A possibilistic knowledge base (KB) is a finite set of such formulas. The problem of revising a possibilistic KB by possibilistic formula is not new. However, existing approaches are limited in two ways. Firstly, they suffer from the so-called drowning effect. Secondly, they handle certain and uncertain formulas separately and most only handle certain inputs. In this paper, we propose a unified approach that caters for revision by both certain and uncertain inputs and relieves the drowning effect. The approach is based on a refined inconsistency degree function called compatibility degree which provides a unifying framework (called cd-revision) for defining specific revision operators for possibilistic KBs. Our definition leads to an algorithm for computing the result of the proposed revision. The revision operators defined in cd-revision possess some desirable properties including those from classic belief revision and some others that are specific to possibilistic revision.We also show that several major revision operators for possibilistic, stratified and prioritised KBs can be embedded in cd-revision.