The modern development in doxastic (and epistemic) logic started with Jaakko HintikkaOs seminal book Knowledge and Belief (1962). In a doxastic logic of Hintikka-type, with a modal operator B standing for Othe agent believes thatO, it is possible to represent and reason about the static aspects of an agentOs beliefs about the world. Such logic studies various constraints that a rational agent or a set of rational agents should satisfy. A Hintikka-type logic cannot, however, be used to reason about doxastic change, i.e., various kinds of doxastic actions that an agent may perform. The agent may, for instance, revise his beliefs by adding a new piece of information, while at the same time making adjustments to his stock of beliefs in order to preserve consistency. Or he may contract his beliefs by giving up a proposition that he formerly believed. Such operations of doxastic change are studied in the theories of rational belief change that started with the work of Alchourrn, Grdenfors and Makinson in the 80Os: the so-called AGM-approach. The theories of belief change developed within the AGM-tradition are not logics in the strict sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language Ð ordinary mathematical English Ð to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal * In this paper we give an informal presentation of some ideas that we have discussed more formally in Lindstrm and Rabinowicz (1997) and (1999). We dedicate it to Peter Grdenfors on his 50th birthday, together with our warmest congratulations and best wishes. Were it not for him, it could never have been written! We wish to thank John Cantwell, Sven Ove Hansson, Tor Sandqvist, and last but not least, Krister Segerberg, for inspiration and advice.
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