Taking Levi Identity Seriously: A Plea for Iterated Belief Contraction

Abstract

Most work on iterated belief change has focused on iterated belief revision, namely how to compute (K $^{\rm *}_{x}$)$^{\rm *}_{y}$. Historically however, belief revision can be defined in terms of belief expansion and belief contraction, where expansion and contraction are viewed as primary operators. Accordingly, our attention to iterated belief change should be focused on constructions like (K $^{\rm +}_{x}$)$^{\rm +}_{y}$, (K $^{\rm --}_{x}$)$^{\rm +}_{y}$, (K $^{\rm +}_{x}$)$^{\rm --}_{y}$ and (K $^{\rm --}_{x}$)$^{\rm --}_{y}$. The first two of these are relatively straightforward, but the last two are more problematic. Here we consider these latter, and formulate iterated belief change by employing the Levi identity and the Harper Identity as the guiding principles.