Epistemic-entrenchment characterization of Parikh's axiom

Abstract

In this article, we provide the epistemicentrenchment characterization of the weak version of Parikh's relevance-sensitive axiom for belief revision - known as axiom (P) - for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemicentrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh's axiom (P).