A Preliminary Study On Logic Of Belief Revision

The classical system of doxastic logic------S_KD45, can model agent's belief and reasoningonly in some static states. In fact, after receiving a new piece of information to the belief set, the epistemic agent will change old belief set. Dynamic epistemic logic(DEL), which merges dynamic logic and epistemic logic, provides formal means of analysis of information change.In this thesis, a logic system will be proposed------dynamic logic of belief revision(DBR),which can model belief change .Part one: As a classical system------S_KD45. it is successful to express strongly the properties of belief: weaker knowledge; positive introspection; negative positive introspection. At the same time, it's false to treat the change and interaction of multi-agent. Sequentially, although belief revision theory conceived by C.Alchourron, P.Gardenfors and D.Mackinson(AGM) treat the change successfully, it is not yet a formal system.Part two: An ordinal conditional function(OCF) expresses a ranking of propositions, and it represents agent's revised belief after receiving a piece of information with firmness a. On the base of OCF, this paper introduces a static logic of belief revision (SBR), including syntax, semantics and proof system. Finally, the logic system is proved complete.Part three: After extending the SBR, by introducing the execution of the action model in epistemic model as a dynamic operator into the logical language, this paper sets up a dynamic logic of belief revision (DBR). It is can be proved that the DBR also is reduced to the SBR, so DBR system is complete too.Part four: I comment on the DBR, and give some problems for further research in the future.