Philosophy Epistemic Philosophy of Logic
Joe Salerno
  • LAST REVIEWED: 29 June 2011
  • LAST MODIFIED: 29 June 2011
  • DOI: 10.1093/obo/9780195396577-0068


Epistemic logic is the study of the principles of inference and the formal semantics of knowledge, belief, and other epistemic notions. This entry discusses the literature in a number of areas therein, including the traditions of treating knowledge and belief with familiar alethic modal logic and possible-world semantics, and of treating these notions in a more dynamic setting that finds its historical roots in belief revision theory (i.e., the formalization of the principles for rational belief updating). This article will also cover special topics, such as the semantics of epistemic modals (that is, epistemic uses of “must,” “might,” “possibly,” etc.) and the semantics of epistemic conditionals (arguably, all indicative “ifs”). We conclude with an overview of important formal (and semiformal) epistemic paradoxes—the most familiar and fundamental epistemic puzzles that demand a formal (or semiformal) treatment.

Epistemic Logic

The origins of modern epistemic logic are found in Wright 1951, where the possibility of modal logics for knowledge and belief are explored, and then developed further in Hintikka 1962. Hintikka’s systematic study of epistemic notions is most commonly paraphrased within the familiar possible-worlds framework. Knowledge (and belief) are treated as a matter of what is true at every epistemically (or doxastically) accessible world. Thinking of Hintikka’s work this way allows for convenient characterization of many different systems of epistemic logic that vary in strength in correspondence with the familiar alethic modals logics (e.g., systems K, D, T, S4 and S5, etc.), substituting the epistemic operators for the alethic ones. One particularly troublesome problem that emerges in this framework is that of logical omniscience. Even in the weakest of the normal modal systems (i.e., system K, replacing necessity operators with knowledge operators), it is a theorem that p is known whenever p is itself a theorem. This is a problem if the logic of knowledge is meant to reflect the logic of the sort of knowledge that we logically non-omniscient humans enjoy. See Lenzen 1978 for a particularly useful early discussion. For a discussion of how epistemic logics have been applied in the sciences, see Meyer 2003. In a separate tradition we find belief revision theory (AGM). See especially Alchourrón, et al. 1985. It was founded on the idea that knowers are active (not static) agents whose knowledge expands, contracts, or is revised in the face of new evidence. Such dynamics were explored widely and in various directions. Van Ditmarsch, et al. 2008 is a textbook that surveys recent theories of epistemic action and belief revision. A concise overview of epistemic logic, belief revision, and dynamic epistemic logic can be found in Hendricks and Symons 2009. For a discussion of the bridge between epistemic logic and mainstream epistemology, see Hendricks and Symons 2006. For another look at the connections between substantive questions in epistemology and the developments in the formal semantics of knowledge, see Stalnaker 2006.

  • Alchourrón, Carlos E., Peter Gärdenfors, and David Makinson. “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions.” Journal of Symbolic Logic 50 (1985): 510–530.

    In this seminal paper, the postulates for rational belief change are developed.

  • Hendricks, Vincent F., and John Symons. “Where’s the Bridge? Epistemology and Epistemic Logic.” Philosophical Studies 128 (2006): 137–167.

    The paper shows where the rich formal developments of epistemic logic of the late 20th and early 21st centuries can be brought to bear fruitfully in contemporary mainstream modal epistemology.

  • Hendricks, Vincent F., and John Symons. “Epistemic Logic.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2009.

    This entry delivers a brief overview of the various movements in modern epistemic logic. It also highlights useful literature on the history of epistemic logic.

  • Hintikka, Jaakko. Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca, NY: Cornell University Press, 1962.

    This influential book offers an early systematic modal treatment of knowledge and belief. It helped to carry the subject of epistemic logic into mainstream epistemology, game theory, economics, and computer science.

  • Lenzen, Wolfgang. “Recent Work in Epistemic Logic.” Acta Philosophica Fennica 30 (1978): 1–219.

    In this paper, the early literature is surveyed. Counterexamples are given to principles such as the KK thesis, that is, the principle that knowing entails knowing that one knows, and solutions to the problem of logical omniscience are canvassed.

  • Meyer, John-Jules Ch. “Modal Epistemic and Doxastic Logic.” In Handbook of Philosophical Logic. Vol. 10. 2d ed. Edited by D. M. Gabbay and F. Guenthner, 1–38. Dordrecht, The Netherlands: Kluwer, 2003.

    Provides an overview of epistemic logics and their applications in computer science and artificial intelligence.

  • Stalnaker, Robert. “On Logics of Knowledge and Belief.” Philosophical Studies 128 (2006): 169–199.

    In this paper, Stalnaker draws lessons for how to inform the formal semantics of knowledge and belief in light of answers to substantive questions in epistemology.

  • van Ditmarsch, Hans, Wiebe van der Hoek, and Barteld Kooi. Dynamic Epistemic Logic. Synthese Library 337. Dordrecht, The Netherlands: Springer, 2008.

    This is a textbook on the latest in dynamic epistemic logic, but it also breaks new ground. The authors develop a model theory for the dynamic epistemic actions that are the focus of their study.

  • Wright, G. H. von. An Essay in Modal Logic. Amsterdam: North-Holland, 1951.

    Among the earliest works to treat knowledge and belief with axiomatic deductive systems, and in particular to apply modal logic to these concepts.

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