Defeasible Justification Using the KLM Framework

Abstract

AbstractThe Kraus, Lehmann and Magidor (KLM) framework is an extension of Propositional Logic (PL) that can perform defeasible reasoning. The results of defeasible reasoning using the KLM framework are often challenging to understand. Therefore, one needs a framework within which it is possible to provide justifications for conclusions drawn from defeasible reasoning. This paper proposes a theoretical framework for defeasible justification in PL and a software tool that implements the framework. The theoretical framework is based on an existing theoretical framework for Description Logic (DL). The defeasible justification algorithm uses the statement ranking required by the KLM-style form of defeasible entailment known as Rational Closure. Classical justifications are computed based on materialised formulas (classical counterparts of defeasible formulas). The resulting classical justifications are converted to defeasible justifications, based on the input knowledge base. We provide an initial evaluation of the framework and the software tool by testing it with a representative example.KeywordsKnowledge representationPropositional logicThe KLM frameworkDefeasible justificationRational closureDefeasible justification tool