Descriptor Revision

Abstract

A descriptor is a set of sentences that are truth-functional combinations of expressions of the form ${\mathfrak{B}p}$ , where ${\mathfrak{B}}$ is a metalinguistic belief predicate and p a sentence in the object language in which beliefs are expressed. Descriptor revision (denoted ${\circ}$) is an operation of belief change that takes us from a belief set K to a new belief set ${K \circ \Psi}$ where ${\Psi}$ is a descriptor representing the success condition. Previously studied operations of belief change are special cases of descriptor revision, hence sentential revision can be represented as ${\Psi = \{\mathfrak{B}p\}}$ , contraction as ${\Psi = \{\neg \mathfrak{B}p\}}$ , multiple contraction as ${\Psi = \{\neg\mathfrak{B}p_1, \neg\mathfrak{B}p_2, \ldots, \neg\mathfrak{B}p_n\}}$ , replacement as ${\Psi = \{\mathfrak{B}p, \neg\mathfrak{B}q\}}$ , etc. General models of descriptor revision are constructed and axiomatically characterized. The common selection mechanisms of AGM style belief change cannot be used, but they can be replaced by choice functions operating directly on the set of potential outcomes (available belief sets). The restrictions of this construction to sentential revision (${\Psi = \{\mathfrak{B}p\} }$) and sentential contraction give rise to operations with plausible properties that are also studied in some some detail.