Two Methods for Constructing Horn Contractions

Abstract

The epistemic entrenchment relation (EE-relation) over sentences and the preference relation (P-relation) over sets of sentences are used for constructing contraction operations in the AGM framework of belief change. The constructed contractions are the epistemic entrenchment based contraction (EEC) and the transitively relational partial meet contraction (TRPMC). Rott [1] establishes a close connection between the two relations and thus the corresponding contractions. It is shown that there is a one-to-one correspondence between TRPMC and EEC thus the two contractions perform identically in the sense that they can be characterised by an identical set of postulates. Recently, belief change for the Horn fragment of classical logic (i.e., Horn logic) has drawn much attention, resulting in several constructions for Horn contractions. In this paper we explore the connections between the two relations under Horn logic. We first define a Horn TRPMC by extending the partial meet Horn contraction defined in [2]. Our investigation shows that, unlike the result established by Rott [1], in Horn logic for each EE-relation there is a corresponding P-relation, but there exist P-relations that have no corresponding EE-relations. As a consequence the corresponding Horn EEC and Horn TRPMC perform differently.