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 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, 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. An Interview with Jaakko Hintikka.E. Arosio - 2000 - Diogenes 48 (192):71-75.
  2. Formal Logic and Practical Reasoning.Bruce Aune - 1986 - Theory and Decision 20 (3):301-320.
    In the past couple of decades several different accounts of the logic of practical reasoning have been proposed.1 The account I have recommended on a number of occasions is clearly the simplest, because it requires no special logical principles, holding that, in respect of deduction, practical reasoning is adequately understood as involving only standard assertoric principles. My account has recently encountered various objections, the most dismissive of which is that it is too simple to deal with complicated cases of practical (...)
  3. Conference Announcement and Call for Papers.Rescher Prize Awarded - 2010 - Review of Metaphysics 64 (1):455.
  4. T.A.F. KUIPERS "Studies in Inductive Probability and Rational Expectation". [REVIEW]D. W. Baird - 1980 - History and Philosophy of Logic 1:247.
  5. Review: John E. Hopcroft, Jeffrey D. Ullman, Relations Between Time and Tape Complexities. [REVIEW]Jiri Becvar - 1973 - Journal of Symbolic Logic 38 (2):343-343.
  6. Announcement.Elizabeth A. Behnke - 1992 - Human Studies 15 (2-3):300-300.
  7. Review: Richard M. Martin, A Formalization of Inductive Logic. [REVIEW]Herbert G. Bohnert - 1969 - Journal of Symbolic Logic 34 (1):137-138.
  8. Belief Change in Branching Time: AGM-Consistency and Iterated Revision. [REVIEW]Giacomo Bonanno - 2012 - Journal of Philosophical Logic 41 (1):201-236.
    We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we (...)
  9. Branching Time, Perfect Information Games and Backward Induction.Giacomo Bonanno - 2001 - Games and Economic Behavior 36 (1):57-73.
    The logical foundations of game-theoretic solution concepts have so far been explored within the con¯nes of epistemic logic. In this paper we turn to a di®erent branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. The branching time framework is extended by adding agents and by de¯ning the notion of prediction. A syntactic characterization of backward induction in terms of the property of internal consistency of prediction (...)
  10. A Note on the Rational Closure of Knowledge Bases with Both Positive and Negative Knowledge.R. Booth & J. B. Paris - 1998 - Journal of Logic, Language and Information 7 (2):165-190.
    The notion of the rational closure of a positive knowledge base K of conditional assertions | (standing for if then normally ) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, | , but (...)
  11. How to Revise a Total Preorder.Richard Booth & Thomas Meyer - 2011 - Journal of Philosophical Logic 40 (2):193 - 238.
    Most approaches to iterated belief revision are accompanied by some motivation for the use of the proposed revision operator (or family of operators), and typically encode enough information in the epistemic state of an agent for uniquely determining one-step revision. But in those approaches describing a family of operators there is usually little indication of how to proceed uniquely after the first revision step. In this paper we contribute towards addressing that deficiency by providing a formal framework which goes beyond (...)
  12. A General Family of Preferential Belief Removal Operators.Richard Booth, Thomas Meyer & Chattrakul Sombattheera - 2012 - Journal of Philosophical Logic 41 (4):711 - 733.
    Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, 2010) (...)
  13. Formalizing Belief Revision in Type Theory.Tijn Borghuis, Fairouz Kamareddine & Rob Nederpelt - 2002 - Logic Journal of the IGPL 10 (5):461-500.
    This paper formalizes belief revision for belief states in type theory. Type theory has been influential in logic and computer science but as far as we know, this is the first account at using type theory in belief revision. The use of type theory allows an agent's beliefs as well as his justifications for these beliefs to be explicitly represented and hence to act as first-class citizens. Treating justifications as first-class citizens allows for a deductive perspective on belief revision. We (...)
  14. Automatic Verification of Temporal-Epistemic Properties of Cryptographic Protocols.Ioana Boureanu, Mika Cohen & Alessio Lomuscio - 2009 - Journal of Applied Non-Classical Logics 19 (4):463-487.
  15. Dynamic Default Logic.Bruce Lee Boyer - 1991 - Dissertation, University of California, Irvine
    Default logics have been extensively studied, primarily by Artificial Intelligence researchers, as a method of representing a form of common sense reasoning. While the motivation of these studies are general founded on intuitive notions of extended modes of inference, the technical work focuses on how to represent the "theory" determined by a set of defaults, ignoring how to actually reason with defaults. ;In this essay I develop a logic which is dynamic in the way "proofs" are produced, reflecting the fact (...)
  16. Declarative Representation of Revision Strategies.Gerhard Brewka - 2001 - Journal of Applied Non-Classical Logics 11 (1-2):151-167.
  17. Nonmonotonic Reasoning From Theoretical Foundation Towards Efficient Computation.Gerhard Brewka - 1989 - [S.N.].
  18. Grim on Logic and Omniscience.Selmer Bringsjord - 1989 - Analysis 49 (4):186 - 189.
  19. Justifications for Common Knowledge.Samuel Bucheli, Roman Kuznets & Thomas Studer - 2011 - Journal of Applied Non-Classical Logics 21 (1):35-60.
  20. Editors' Announcement.Charles Capper, Anthony La Vopa & Samuel Moyn - 2011 - Modern Intellectual History 8 (2):265-265.
  21. Lemmon E. J.. On Sentences Verifiable by Their Use. Analysis , Vol. 22 No. 4 , Pp. 86–89.Hintikka Jaakko. Cogito, Ergo Sum: Inference or Performance? The Philosophical Review, Vol. 71 , Pp. 3–32. [REVIEW]James Cargile - 1969 - Journal of Symbolic Logic 33 (4):615-616.
  22. Belief Revision 1 Thinking and Reasoning, 2001, 7, 217 234 Belief Revision and Uncertain Reasoning Guy Politzer CNRS, SaintDenis. [REVIEW]Laure Carles - 2001 - Thinking and Reasoning 7:217-234.
  23. Pluralistic Ignorance and Collective Belief: A DDL Approach.Proietti Carlo - forthcoming - Journal of Philosophical Logic.
  24. Stdies in Inductive Logic and Probability.Rudolf Carnap - 1975 - Journal of Symbolic Logic 40 (4):581-583.
  25. A Basic System of Inductive Logic, Part I.Rudolf Carnap - 1971 - In Richard Jeffrey & Rudolf Carnap (eds.), Studies in Inductive Logic and Probability. University of California Press: Los Angeles. pp. 34--165.
  26. The Nature and Application of Inductive Logic, Consisting of Six Sections From: Logical Foundations of Probability.Rudolf Carnap - 1951 - Journal of Symbolic Logic 16 (4):287-287.
  27. Inductive Logic and Inductive Intuition.Rudolf Carnap, M. Bunge, J. W. N. Watkins, Y. Bar-Hillel, K. R. Popper & J. Hintikka - 1975 - Journal of Symbolic Logic 40 (3):449-450.
  28. Hintikka Jaakko. Knowledge and Belief. An Introduction to the Logic of the Two Notions. Cornell University Press, Ithaca, N.Y., 1962, X + 179 Pp. [REVIEW]Hector-Neri Castañeda - 1964 - Journal of Symbolic Logic 29 (3):132-134.
  29. 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 (...)
  30. Referential Opacity and Epistemic Logic.Saloua Chatti - 2011 - Logica Universalis 5 (2):225-247.
    Referential opacity is the failure of substitutivity of identity (SI, for short) and in Quine’s view of existential generalization (EG, for short) as well. Quine thinks that its “solution” in epistemic and doxastic contexts, which relies on the notion of exportation, leads to undesirable results. But epistemic logicians such as Jaakko Hintikka and Wolfgang Lenzen provide another solution based on a different diagnosis: opacity is not, as in Quine’s view, due to the absence of reference, it is rather due to (...)
  31. 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. (...)
  32. Approximate Belief Revision.S. Chopra, R. Parikh & R. Wassermann - 2001 - Logic Journal of the IGPL 9 (6):755-768.
    The standard theory for belief revision provides an elegant and powerful framework for reasoning about how a rational agent should change its beliefs when confronted with new information. However, the agents considered are extremely idealized. Some recent models attempt to tackle the problem of plausible belief revision by adding structure to the belief bases and using nonstandard inference operations. One of the key ideas is that not all of an agent's beliefs are relevant for an operation of belief change.In this (...)
  33. Iterated Belief Change and the Recovery Axiom.Samir Chopra, Aditya Ghose, Thomas Meyer & Ka-Shu Wong - 2008 - Journal of Philosophical Logic 37 (5):501-520.
    The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem (...)
  34. Putting Logic in its Place: Formal Constraints on Rational Belief.David Christensen - 2004 - Oxford University Press.
    What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.
  35. Review: Rudolf Carnap, Notes for Symbolic Logic. [REVIEW]Alonzo Church - 1939 - Journal of Symbolic Logic 4 (1):29-30.
  36. Review: Rudolf Carnap, On the Application of Inductive Logic. [REVIEW]C. West Churchman - 1948 - Journal of Symbolic Logic 13 (2):120-121.
  37. Bergmann Gustav. Some Comments on Carnap's Logic of Induction. Philosophy of Science, Vol. 13 Pp. 71–78.C. West Churchman - 1946 - Journal of Symbolic Logic 11 (3):81.
  38. 526 Announcements.Francis P. Coolidge Jr - 2009 - Review of Metaphysics 63:525-526.
  39. Non-Monotonic Reasoning in a Semantic Network.Marcel Cori - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 239--248.
  40. Free Quantified Epistemic Logics.Giovanna Corsi & Eugenio Orlandelli - 2013 - Studia Logica 101 (6):1159-1183.
    The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.
  41. Logic, Deductive and Inductive.Thomas Crumley - 1934 - New York: the Macmillan Company.
  42. Inductive Logic.Vincenzo Crupi - 2015 - Journal of Philosophical Logic 44 (6):641-650.
    The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...)
  43. Confirmation as Partial Entailment: A Representation Theorem in Inductive Logic.Vincenzo Crupi & Katya Tentori - 2013 - Journal of Applied Logic 11 (4):364-372.
  44. Review: Henryk Greniewski, Elements of the Logic of Induction. [REVIEW]Zbigniew Czerwinski - 1958 - Journal of Symbolic Logic 23 (1):77-78.
  45. On the Logic of Iterated Belief Revision.Adnan Darwiche & Judea Pearl - 1997 - Artificial Intelligence 89:1-29.
    We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...)
  46. Greenwood David. Quantitative Inductive Procedures. The Nature of Science and Other Essays, by Greenwood David, Philosophical Library, New York 1959, Pp. 32–43. [REVIEW]Edward E. Dawson - 1996 - Journal of Symbolic Logic 31 (3):494-496.
  47. Non Monotonic Reasoning and Belief Revision: Syntactic, Semantic, Foundational and Coherence Approaches.Alvaro Del Val - 1997 - Journal of Applied Non-Classical Logics 7 (1-2):213-240.
  48. Gricean Belief Change.James P. Delgrande, Abhaya C. Nayak & Maurice Pagnucco - 2005 - Studia Logica 79 (1):97-113.
    One of the standard principles of rationality guiding traditional accounts of belief change is the principle of minimal change: a reasoner's belief corpus should be modified in a minimal fashion when assimilating new information. This rationality principle has stood belief change in good stead. However, it does not deal properly with all belief change scenarios. We introduce a novel account of belief change motivated by one of Grice's maxims of conversational implicature: the reasoner's belief corpus is modified in a minimal (...)
  49. Announcement.J. Demongeot - 1988 - Acta Biotheoretica 37 (3-4):103-103.
  50. Announcement.Eliot Deutsch - 1972 - Southern Journal of Philosophy 10 (3):i-i.
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