Coherence and Conservatism in the Dynamics of Belief II: Iterated Belief Change without Dispositional Coherence

Part I of this paper Rott has argued that doxastic states should be repre sented as revision functions that take sequences of sentences of arbitrary nite length as arguments and return belief sets that is sets of sentences closed under some background logic Cn as a result We have interpreted the well known rationality postulates for belief change given by Alchourr on G ardenfors and Makinson and isolated three independent concepts of coherence that are partially encoded by them We noticed that contrary to the common opin ion the classic theory expounded by these authors and further developed by many more writers does not o er a substantial account of the idea of minimal changes of belief This idea which is also known as conservatism embodies a diachronic conception of coherence In the belief revision theory of Alchourr on G ardenfors and Makinson henceforth AGM a much more important role is played by what I call synchronic coherence or inferential coherence or re ective equilibrium roughly logical consistency and closure of belief sets and disposi tional coherence The latter concept nds expression in AGM s supplementary revision postulates and is equivalent to the rationalizability of the revision be haviour by some very well behaved choice function viz one that can be obtained by maximization with respect to a transitive preference ordering Representation theorems showing that such equivalences do in fact obtain may justly be called the core of the AGM paradigm