Sentential Revision

• Sven Ove Hansson
Chapter
Part of the Trends in Logic book series (TREN, volume 46)

Abstract

This is the first of three chapters in which the major traditional belief change operations, namely (sentential) revision and contraction, are constructed as special cases of descriptor revision. In both its local and global forms, sentential revision $$(*)$$ can be constructed with the simple formula $$K*p= K\circ \mathfrak {B}p$$. Two axiomatic characterizations show how the properties of the derived operation $$*$$ depend on those of the underlying descriptor revision $$\circ$$. The most important results in this chapter are two theorems showing that the major revision operations of AGM, namely partial meet revision and its transitively relational variant, are both reconstructible as subcases of sentential revision in the descriptor framework. In other words, both these classes of sentential revision $$(*)$$ coincide with operations obtained with the defining formula $$K*p= K\circ \mathfrak {B}p$$ from certain classes of descriptor revision $$(\circ )$$ that are identified here. These results provide important connections between AGM revision and the more general category of descriptor revision. Furthermore, they provide useful insights into the properties of the AGM operations. The chapter also investigates relations of believability, i.e. the relations on sentences that are obtainable from relations of epistemic proximity on descriptors (see Chapter ) according to the simple principle that p is more believable than q if and only if $$\mathfrak {B}p$$ is epistemically more proximate than $$\mathfrak {B}q$$. Finally, some results are presented on multiple sentential revision, i.e. simultaneous revision by several sentences, and on the operation of making up one’s mind.