Edited by Mark Jago (Nottingham University)
|Summary||Epistemic logics are logics that allow one to reason about knowledge in some way. Doxastic logics are similar, but allow one to reason about belief rather than knowledge. The languages of these logics contain knowledge or belief operators or predicates, governed by appropriate axioms or rules. (Just what axioms and rules are appropriate is a controversial matter, however.) Many epistemic and doxastic logics are modal logics, whose languages contains one or more knowledge or belief operators, and whose semantics is given in terms of relational Kripke models. In such models, the points or states can be thought of as epistemically (or doxastically) possible worlds, related to one another by epistemic (or doxastic) accessibility relations. This modal approach to epistemic and doxastic logic has been widely adopted in formal logic, philosophy, computer science, artificial intelligence, economics and game theory. The category doxastic logic also includes work on belief revision and belief update, which addresses the question: how should an agent revise or update its beliefs, on receiving conflicting information?|
|Key works||Modern epistemic logic began with Hintikka 1962, who developed Kripke-style semantics for epistemic notions and discussed appropriate axioms for knowledge and belief. Hintikka proposes a solution to the logical omniscience problem, whereby agents are treated as automatically knowing all consequences of what they know, in Hintikka 1975. Hintikka's approach is developed and applied to problems in computer science in Fagin et al 1995. The leading theory of belief revision, the ‘AGM’ theory, was first presented in Alchourrón et al 1985.|
|Introductions||Hintikka 1962 is a great introduction to epistemic and doxastic logics; Hendricks 2008 briefly surveys the area. Huber 2013 introduces and discusses AGM theories of belief revision.|
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