Inducing Inference Relations from Inconsistency Measures

Xiaolong Liu, Philippe Besnard, Sylvie Doutre

Abstract: This article defines a family of inference relations which aim at reasoning with inconsistent knowledge bases. These inference relations are defined out of inconsistency measures. We check under which conditions the new inference relations satisfy a series of properties for nonmonotonic reasoning. We also show that they are paraconsistent when the corresponding inconsistency measures satisfy some rationality postulates. Besides, we show some dependencies and incompatibilities among some rationality postulates.