Distance Semantics for Relevance-Sensitive Belief Revision Extended Abstract

The AGM postulates [4], [1] are widely regarded to have captured much of what is involved in the process of rational belief revision. Recently however, Parikh [7] observed that despite their success, the AGM postulates are rather liberal in their treatment of the notion of relevance. More precisely, Parikh argues that during belief revision a rational agent does not change her entire belief corpus, but only the portion of it that is relevant to the new information. This intuition of local change, Parikh claims, is not fully captured by the AGM postulates. To remedy this shortcoming, Parikh introduced an additional axiom, named (P), as a supplement to the AGM postulates. Loosely speaking, axiom (P) says that when new information φ is received, only part of the initial belief set K will be affected; namely the part that shares common propositional variables with the minimal language of φ. Parikh’s approach is also known as the language splitting model. Our main goal in this paper is to provide possible-world semantics for axiom (P). In particular, we examine new constraints on systems of spheres and, building on Grove’s representation result [5], we prove that in the presence of the AGM postulates, axiom (P) is sound and complete with respect to these new semantic constraints. What is particularly pleasing about our result is that the new constraints on systems of spheres are in fact not new at all; they essentially generalize a very natural condition that predates axiom (P) and has been motivated independently by Winslett in the context of Reasoning about Action [12]. In the course of formulating semantics for axiom (P) we observed that there are in fact two possible readings of this axiom, which we call the strong and the weak versions of (P). In the full text of this article, [10], both versions are studied. Herein however we confine the discussion to the weak version of axiom (P).