Towards a ‘sophisticated’ model of belief dynamics

It has been often noted that classical models of belief do not accurately represent the limits of human doxastic capacity, at least if belief is understood in a sufficiently internal sense. This is equally true of models of belief revision (Hansson, 2003). Furthermore, Rott (2004) has recently raised doubts about several of the most important of Gärdenfors postulates relating to belief revision; he called for a " more sophisticated model of belief formation ". This paper is attempt to tackle some of these challenges. It proposes a model of belief states which (1) is faithful to a certain finiteness of human doxastic capabilities, whilst at the same time (2) permitting a general model for iterated belief revision which (2a) satisfies the basic G¨ardenfors postulates for belief revision and (2b) reproduces several of the suggested notions of iterated belief revision as 'special cases'. Finally (3), it provides a natural analysis of Rott's supposed counterexample, in terms of a 'framing effect' which is easily modeled in the proposed framework. The fundamental observation behind the proposal is the importance of the notion of a sentence or an issue which is 'in play' at a particular moment. This observation seems pertinent not only to certain cases of failure of logical omniscience, but equally to cases of 'overlooked' beliefs. For example, if the agent forgets to go to his meeting at 10.00, it is not that at 10.00 he believes there is no meeting, nor that at 10.00 he neither believes that there is a meeting nor that there is no meeting, but rather that the subject of the meeting doesn't 'enter into his mind', or it doesn't enter 'into play'. A simple way of accommodating the notion of being (or not) 'in play' is to explicitly specify the sentences involved at a given moment, and permit this set of 'pertinent' sentences to change with time. A 'local ' language , or at least a 'local fragment' of language, with its own 'local' logical structure (notion of logical equivalence between its sentences, and so on), will be 'operational' or 'relevant' at a given moment; the only beliefs which are explicit or active at that moment are those towards the sentences of this local language. However, we will not follow the proposals of Fagin and Halpern (1988), which effectively consist in taking the ordinary possible worlds belief framework and adding appropriate restrictions on the belief operator …