Revision and Update Based on Stratified Forward Chaining

Abstract

In this work we reconsider some of the properties of nonmonotonic logic [Gab-bay, 1985; Kraus et al., 1990] and change operators [Alchourrón et al., 1985; Katsuno and Mendelzon, 1990; Darwiche and Pearl, 1994] which were established using classical logic as being the object language in a less rich framework but yet enough expressive to consider some interesting situations. Pieces of knowledge are represented as literals and rules. The inference engine we propose to represent the underlying logic of the agent is based on an ordered stratification of the set of literals appearing in the knowledge base which consists of a finite set of rules. Given such a stratification, elementary forward chaining steps are achieved along its strata starting from the first one which is taken to be the input set of literals (the basic facts). The literals generated this way are combined in such a way that the specific information is privileged over less specific information when they conflict each other. Forward chaining allows for efficient computations as it is the case with inheritance systems which are known to be efficient nonmonotonic systems. An eminent property of stratified forward chaining is Consistency Preservation which makes the consistency of the consequences depend only on the consistency of the set of literals which the inference operation starts from.