Around a powerful property of circumscriptions

Abstract

The notion of preferential entailment has emerged as a generalization of circumscription. Here we study only “classical” preferential entailment, i.e. the underlying logic is classical. Also, as we want to apply these results to the various notions of circumscriptions which have been defined in the literature, we examine which preferential entailments can be considered as a kind of circumscription. Among the results given are a precise study of cumulativity (with respect to well-foundedness), even for preferential entailments based on non transitive relations, and the isolation of a property called “reverse monotony”, which is a fundamental characteristic of any preferential entailment associated to a circumscription. We prove that the main properties of circumscriptions can be considered as corollaries of reverse monotony. We introduce also a new property of circumscriptions, “disjunctive coherence”, which is not a consequence of reverse monotony.