Tableaux for expansion and contraction

Abstract

The classical AGM account (Alchourrón, Gärdenfors and Makinson [1985]) of belief revision is an account of the process of changing sets of beliefs by either adding beliefs consistent with a belief set (expansion), or giving up beliefs (contraction). The AGM account is built on the notion of classically consistent theories which are closed under deductive consequence and include all the theorems of their base logic. We present an account of belief sets and belief change in terms of model-sets (Hintikka [1969]) and tableaux with flagged formulas. The account is four valued rather than two valued, and uses the values true, not true, false and not false. These are “believed” values. The account allows for paraconsistency. We draw on the semi-classical logics around RM (Dunn [1976]). The use of flagged formulas allows for a more subtle approach to both expansion and contraction.