The Basic Dynamic Doxastic Logic of AGM

Abstract

As pointed out by Hans Rott and others, there are two ways of reading AGM, the theory of Alchourrón, Gärdenfors and Makinson presented in a classic paper that has come to be regarded as the fons et origo of today’s formal study of belief revision [Alchourrón et al., 1985]. Under the “iterative” reading there is room for multiple sequential belief change, but under the “one-shot” reading the perspective is limited to one change. Roughly and informally, the “one-shot” reading recognizes doxastic situations of two kinds. First, there is status quo, the (generic but unique) anterior situation. Then a belief change takes place, landing the agent in a posterior situation. And this is the entire scenario! There is no inkling that there could be further belief changes and corresponding post-posterior situations. Iterative theories are richer and more interesting. But as they are more difficult to devise, one might begin by studying one-shot theories (to which from now on we will refer without scare quotes). In this paper, we suggest how one-shot AGM can be rendered within dynamic doxastic logic (DDL). This author’s first effort in this area was [Segerberg, 1994a], but only with van Linder, van der Hoek and Meyer [1995] did we get a faithful interpretation of AGM in a DDL language (that is, a model theoretical analysis of Gärdenfors’s characterization in [1988) of the three main doxastic operations: expansion, contraction, and revision of belief sets). However, in neither paper was the question of a complete axiomatization of the set of valid formulæ addressed; here, it is.