Local Descriptor Revision

Abstract

In this chapter the properties of descriptor revision, as defined in Chapter 4, are further explored. Several alternative selection mechanisms are presented, and the properties of the resulting operations are investigated. In one of these variants, the choice function is based on a relation on belief sets that can be interpreted as representing distances from the current belief set. In another, descriptor revision is constructed from a blockage relation on the outcome set (set of potential outcomes). A belief set blocks another belief set if the latter is ineligible as a revision outcome whenever the first is available. The different variants of descriptor revision are axiomatically characterized with plausible postulates. The controversial axioms discussed in Chapter 3 do not hold in the new framework. Finally, a binary relation on descriptors, the relation of epistemic proximity, is introduced. A descriptor is more epistemically proximate than another descriptor if some belief set satisfying it is closer at hand for the agent, or it can be satisfied with a less far-reaching change. For instance, \(\mathfrak {B}_p \succeq \lnot \mathfrak {B}_q\) denotes that it is closer at hand for the epistemic agent to believe in p than not to believe in q. Relations of epistemic proximity (between descriptors) generalize the relations of epistemic entrenchment (between sentences) that have been developed in the AGM framework. The translation is straight-forward: p is less entrenched than q if and only if \(\lnot \mathfrak {B}_p\) is more proximate than \(\lnot \mathfrak {B}_q\). The chapter also contains a section about indeterministic descriptor revision, in which the operation does not specify a single outcome for each input, but only a set of possible outcomes.