Horn Contraction via Epistemic Entrenchment

Abstract

Belief change studies the way in which a reasoner should maintain its beliefs in the face of newly acquired information. The AGM account of belief change assumes an underlying logic containing classical propositional logic. Recently, there has been interest in studying belief change, specifically contraction, under the Horn fragment of propositional logic (i.e., Horn logic). In this paper we continue this line of research, and propose a Horn contraction that is based on the Epistemic Entrenchment (EE) construction of AGM contraction. The standard EE construction refers to arbitrary disjunctions which are not available in Horn logic. Therefore, we make use of a Horn approximation technique called Horn strengthening. An ideal Horn contraction should be as plausible as an AGM contraction. In other words it should performs identically with AGM contractions when restricted to Horn logic. We demonstrate that no EE based Horn contraction satisfies this criterion unless we apply certain restrictions to the AGM contraction. A representation theorem is proved which identifies the characterising postulates for our Horn contraction.