Edited by Mark Jago (Nottingham University)
|Summary||Epistemic logics are logics that allow one to reason about knowledge in some way. The term ‘epistemic logic’ is often applied also to logics of related notions, such as logics of belief (more strictly, doxastic logics) and justification. Many epistemic logics are modal logics, whose language contains one or more knowledge operators and whose semantics is given in terms of relational Kripke models, containing epistemically possible worlds related to one another by epistemic accessibility relations. This modal approach to epistemic logic has been widely adopted in formal logic, philosophy, computer science, artificial intelligence, economics and game theory. The sub-sategory ‘Doxastic and Epistemic Logic’ also includes formal work on belief revision. This category also includes inductive logics and non-monotonic logics, both of which add to the stock of valid inferences, beyond those valid in classical logic. (These logics are super-classical, containing inferences which are not deductively valid and hence, in some sense, less than certain. In such logics, there is no guarantee that truth will be preserved from premises to conclusions. Non-monotonic logics have the feature that an inference from premises X to conclusion A may be valid, and yet the inference to A may fail if we add an addition premise B to X, so that X ⊢ A but not X, B ⊢ A.|
|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. Key early works in inductive logic are Keynes 1929 and Carnap’s 1945, 1952, 1962. Key early works in non-monotonic logic are Moore 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. Hawthorne 2011 and Huber 2007 are good encyclopaedia entries on inductive logic; Hacking 2001 is a book-length introduction. Antonelli 2008 is a good, brief introduction to non-monotonic logic; an excellent book-length treatment is Makinson 2005.|
Doxastic and Epistemic Logic
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