Iterated Belief Contraction from First Principles

Abhaya C. Nayak, Randy Goebel, Mehmet A. Orgun

Importance of contraction for belief change notwithstanding, literature on iterated belief change has by and large centered around the issue of iterated belief revision, ignoring the problem of iterated belief contraction. In this paper we examine iterated belief contraction in a principled way, starting with Qualified Insertion, a proposal by Hans Rott. We show that a judicious combination of Qualified Insertion with a well-known Factoring principle leads to what is arguably a pivotal principle of iterated belief contraction. We show that this principle is satisfied by the account of iterated belief contraction modelled by Lexicographic State Contraction, and outline its connection with Lexicographic Revision, Darwiche-Pearl's account of revision as well as Spohn's Ordinal ranking theory. Keywords: Belief Change, Information State Change, Iterated Belief Contraction.