About this topic
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 may fail if we add an addition premise B to X, so that XA 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 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, 19521950. 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
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  1. A New Framework for Epistemic Logic.Yanjing Wang - 2017 - In Proceedings of TARK 2017. EPTCS. pp. 515-534.
    Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we (...)
  2. Beyond Knowing That: A New Generation of Epistemic Logics.Yanjing Wang - 2018 - In Hans Van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Springer. pp. 499-533.
    Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka [58]. Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of “knowing that”. However, knowledge is expressed in everyday life by using various other locutions such as “knowing whether”, “knowing what”, “knowing how” and so on (knowing-wh hereafter). Such knowledge expressions (...)
  3. True Lies.Thomas Ågotnes, Hans van Ditmarsch & Yanjing Wang - 2018 - Synthese 195 (10):4581-4615.
    A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula that becomes true when announced. We investigate true lies and other types of interaction between announced formulas, their preconditions and their postconditions, in the setting of Gerbrandy’s logic of believed announcements, wherein agents may have or obtain incorrect beliefs. Our results are on the satisfiability and validity of instantiations of these semantically (...)
  4. Higher-Order Uncertainty.Kevin Dorst - forthcoming - In Mattias Skipper & Asbjørn Steglich Petersen (eds.), Higher-Order Evidence: New Essays.
    You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of disagreement. Third, the answer is (...)
  5. Probabilistic Justification Logic.Joseph Lurie - 2018 - Philosophies 3 (1):2-0.
    Justification logics are constructive analogues of modal logics. They are often used as epistemic logics, particularly as models of evidentialist justification. However, in this role, justification logics are defective insofar as they represent justification with a necessity-like operator, whereas actual evidentialist justification is usually probabilistic. This paper first examines and rejects extant candidates for solving this problem: Milnikel’s Logic of Uncertain Justifications, Ghari’s Hájek–Pavelka-Style Justification Logics and a version of probabilistic justification logic developed by Kokkinis et al. It then proposes (...)
  6. Some Connections Between Epistemic Logic and the Theory of Nonadditive Probability.Philippe Mongin - 1992 - In Paul Humphreys (ed.), Patrick Suppes: Scientific Philosopher. Dordrecht: Kluwer. pp. 135-171.
    This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic of belief change (...)
  7. Toward Predicate Approaches to Modality.Johannes Stern - 2016 - Switzerland: Springer.
    In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. -/- The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach (...)
  8. "Knowing Value" Logic as a Normal Modal Logic.Tao Gu & Yanjing Wang - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 362-381.
  9. Conditionally Knowing What.Yanjing Wang & Jie Fan - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 569-587.
  10. Indicative Conditionals and Dynamic Epistemic Logic.Wesley H. Holliday & Thomas Icard - 2017 - Proceedings of the Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017.
    Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...)
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  11. The Irreducibility of Iterated to Single Revision.Jake Chandler & Richard Booth - 2017 - Journal of Philosophical Logic 46 (4):405-418.
    After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a (...)
  12. An Abstract Approach to Reasoning About Games with Mistaken and Changing Beliefs.Benedikt Löwe & Eric Pacuit - 2008 - Australasian Journal of Logic 6:162-181.
    We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour in games (...)
  13. R. M. Martin’s Logic of Belief.David Parsons - 2017 - History and Philosophy of Logic 38 (1):72-86.
    In this paper I revisit R. M. Martin’s logic of belief. As with much of Martin’s work, his formal studies into belief and belief reports have gone largely unnoticed. However, in my article I suggest reasons for thinking that these studies warrant revisiting. One reason is that Martin adopted an account of the notion of belief which was more comprehensive than that employed by most rival theorists. Another reason is that Martin couched his theory in a formal pragmatics which utilised (...)
  14. Logical Tools for Human Thinking: Jaakko Hintikka.Ilkka Niiniluoto - 2016 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (2):267-276.
    One of the many research projects of Jaakko Hintikka was entitled “Logical tools for human thinking and their history”. This is in fact an apt summary of the lifetime work of this master logician who developed several new methods and systems in mathematical and philosophical logic, among them distributive normal forms, model sets, possible-worlds semantics, epistemic logic, doxastic logic, inductive logic, semantic information, game-theoretical semantics, interrogative approach to inquiry, and independence-friendly logic. He applied them to study problems in philosophy of (...)
  15. Propositional Quantification in Logics of Contingency.Hans van Ditmarsch & Jie Fan - 2016 - Journal of Applied Non-Classical Logics 26 (1):81-102.
    In this work we define contingency logic with arbitrary announcement. In contingency logic, the primitive modality contingency formalises that a proposition may be true but also may be false, so that if it is non-contingent then it is necessarily true or necessarily false. To this logic one can add dynamic operators to describe change of contingency. Our logic has operators for public announcement and operators for arbitrary public announcement, as in the dynamic epistemic logic called arbitrary public announcement logic. However, (...)
  16. Epistemic Logic Meets Epistemic Game Theory: A Comparison Between Multi-Agent Kripke Models and Type Spaces.Paolo Galeazzi & Emiliano Lorini - 2016 - Synthese 193 (7):2097-2127.
    In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers :149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42:863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison between (...)
  17. A Computationally Grounded, Weighted Doxastic Logic.Taolue Chen, Giuseppe Primiero, Franco Raimondi & Neha Rungta - 2016 - Studia Logica 104 (4):679-703.
    Modelling, reasoning and verifying complex situations involving a system of agents is crucial in all phases of the development of a number of safety-critical systems. In particular, it is of fundamental importance to have tools and techniques to reason about the doxastic and epistemic states of agents, to make sure that the agents behave as intended. In this paper we introduce a computationally grounded logic called COGWED and we present two types of semantics that support a range of practical situations. (...)
  18. Announcement.Sander Griffioen - 1989 - Philosophia Reformata 54 (2):197-197.
  19. Book Announcements.J. van der Stoep - 2004 - Philosophia Reformata 69 (2):207-208.
  20. Book Announcements.J. van der Stoep - 2004 - Philosophia Reformata 69 (1):111-112.
  21. A Simple Nonmonotonic Logic as a Model of Belief Change.Masaharu Mizumoto - 2003 - Annals of the Japan Association for Philosophy of Science 12 (1):25-52.
  22. A Bi-Modal Characterization of Epistemic Logic.Arata Ishimoto - 1978 - Annals of the Japan Association for Philosophy of Science 5 (3):135-155.
  23. First Steps Towards Probabilistic Justification Logic.Ioannis Kokkinis, Petar Maksimović, Zoran Ognjanović & Thomas Studer - 2015 - Logic Journal of the IGPL 23 (4):662-687.
  24. Connecting Dynamic Epistemic and Temporal Epistemic Logics.H. van Ditmarsch, W. van der Hoek & J. Ruan - 2013 - Logic Journal of the IGPL 21 (3):380-403.
  25. Megiddo Nimrod and Wigderson Avi. On Play by Means of Computing Machines . Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 259–274.Gaifman Haim. A Theory of Higher Order Probabilities. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 275–292.Micali Silvio. Knowledge and Efficient Computation. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 353–362. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):669-670.
  26. Konolige Kurt. What Awareness Isn't: A Sentential View of Implicit and Explicit Belief. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 241–250. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):667-668.
  27. Lakemeyer Gerhard. Steps Towards a First-Order Logic of Explicit and Implicit Belief. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 325–340. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):668.
  28. Martins João P. And Shapiro Stuart C.. Theoretical Foundations for Belief Revision. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 383–398. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):669.
  29. Smullyan Raymond M.. Logicians Who Reason About Themselves. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 341–352. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):668-669.
  30. Vardi Moshe Y.. On Epistemic Logic and Logical Omniscience. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 293–305. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):668.
  31. Asher Nicholas M. And Kamp Johan A. W.. The Knower's Paradox and Representational Theories of Attitudes. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 131–147. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):666.
  32. Dwork Cynthia and Moses Yoram. Knowledge and Common Knowledge in a Byzantine Environment I: Crash Failures. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 149–169. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):666.
  33. Fagin Ronald and Vardi Moshe Y.. Knowledge and Implicit Knowledge in a Distributed Environment: Preliminary Report. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 187–206. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):667.
  34. Ladner Richard E. And Reif John H.. The Logic of Distributed Protocols . Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 207–222. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):667.
  35. Morgenstern Leora. A First Order Theory of Planning, Knowledge, and Action. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 99–114. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):664-665.
  36. Rivières Jim Des and Levesque Hector J.. The Consistency of Syntactical Treatments of Knowledge. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 115–130. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):665-666.
  37. Hintikka Jaakko. Reasoning About Knowledge in Philosophy: The Paradigm of Epistemic Logic. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 63–80. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):663-664.
  38. Halpern Joseph Y.. Reasoning About Knowledge: An Overview. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 1–17. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):660-661.
  39. Landman Fred. Pegs and Alecs. An Abridged Version of LIII 656. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 45–61. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):662-663.
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  41. Smith Brian Cantwell. Varieties of Self-Reference. Theoretical Aspects of Reasoning About Knowledge, Proceedings of the 1986 Conference, Edited by Halpern Joseph Y., Morgan Kaufmann Publishers, Los Altos 1986, Pp. 19–43. [REVIEW]William J. Rapaport - 1988 - Journal of Symbolic Logic 53 (2):661-662.
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