About this topic
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 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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  1. Future Determination of Entities in Talmudic Public Announcement Logic.M. Abraham, I. Belfer, D. M. Gabbay & U. Schild - 2013 - Journal of Applied Logic 11 (1):63-90.
  2. What Will They Say?—Public Announcement Games.Ågotnes Thomas & Ditmarsch Hans van - 2011 - Synthese 179 (S1):57 - 85.
    Dynamic epistemic logic describes the possible information-changing actions available to individual agents, and their knowledge pre-and post conditions. For example, public announcement logic describes actions in the form of public, truthful announcements. However, little research so far has considered describing and analysing rational choice between such actions, i.e., predicting what rational self-interested agents actually will or should do. Since the outcome of information exchange ultimately depends on the actions chosen by all the agents in the system, and assuming that agents (...)
  3. The Undecidability of Quantified Announcements.T. Ågotnes, H. van Ditmarsch & T. French - 2016 - Studia Logica 104 (4):597-640.
    This paper demonstrates the undecidability of a number of logics with quantification over public announcements: arbitrary public announcement logic, group announcement logic, and coalition announcement logic. In APAL we consider the informative consequences of any announcement, in GAL we consider the informative consequences of a group of agents all of which are simultaneously making known announcements. So this is more restrictive than APAL. Finally, CAL is as GAL except that we now quantify over anything the agents not in that group (...)
  4. A Logic for Reasoning About Knowledge of Unawareness.Thomas Ågotnes & Natasha Alechina - 2014 - Journal of Logic, Language and Information 23 (2):197-217.
    In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo introduced a logic (...)
  5. Group Announcement Logic.Thomas Ågotnes, Philippe Balbiani, Hans van Ditmarsch & Pablo Seban - 2010 - Journal of Applied Logic 8 (1):62-81.
  6. Tableau-Based Decision Procedure for the Multiagent Epistemic Logic with All Coalitional Operators for Common and Distributed Knowledge.M. Ajspur, V. Goranko & D. Shkatov - 2013 - Logic Journal of the IGPL 21 (3):407-437.
    We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi\-agent epistemic logic \CMAELCD\ with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for \CMAELCD\ and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set of (...)
  7. Tableaux-Based Decision Method for Single-Agent Linear Time Synchronous Temporal Epistemic Logics with Interacting Time and Knowledge.Mai Ajspur & Valentin Goranko - 2013 - In Kamal Lodaya (ed.), Logic and its Applications. Springer. pp. 80--96.
    Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time and (...)
  8. About Cut Elimination for Logics of Common Knowledge.Luca Alberucci & Gerhard Jäger - 2005 - Annals of Pure and Applied Logic 133 (1):73-99.
    The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of these (...)
  9. The Intuitive Background of Normative Legal Discourse and its Formalization.Carlos E. Alchourrón - 1972 - Journal of Philosophical Logic 1 (3/4):447 - 463.
  10. A Logic of Situated Resource-Bounded Agents.Natasha Alechina & Brian Logan - 2009 - Journal of Logic, Language and Information 18 (1):79-95.
    We propose a framework for modelling situated resource-bounded agents. The framework is based on an objective ascription of intentional modalities and can be easily tailored to the system we want to model and the properties we wish to specify. As an elaboration of the framework, we introduce a logic, OBA, for describing the observations, beliefs, goals and actions of simple agents, and show that OBA is complete, decidable and has an efficient model checking procedure, allowing properties of agents specified in (...)
  11. Verifying Time, Memory and Communication Bounds in Systems of Reasoning Agents.Natasha Alechina, Brian Logan, Hoang Nga Nguyen & Abdur Rakib - 2009 - Synthese 169 (2):385-403.
    We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its (...)
  12. Logic, Reasoning and Revision.Patrick Allo - 2016 - Theoria 82 (1):3-31.
    The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...)
  13. Adaptive Logic as a Modal Logic.Patrick Allo - 2013 - Studia Logica 101 (5):933-958.
    Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, (...)
  14. The Many Faces of Closure and Introspection.Patrick Allo - 2013 - Journal of Philosophical Logic 42 (1):91-124.
    In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.
  15. The Logic of 'Being Informed' Revisited and Revised.Patrick Allo - 2011 - Philosophical Studies 153 (3):417-434.
    The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, and tries to find out (...)
  16. Reasoning About Data and Information.Patrick Allo - 2009 - Synthese 167 (2):231-249.
    Cognitive states as well as cognitive commodities play central though distinct roles in our epistemological theories. By being attentive to how a difference in their roles affects our way of referring to them, we can undoubtedly accrue our understanding of the structure and functioning of our main epistemological theories. In this paper we propose an analysis of the dichotomy between states and commodities in terms of the method of abstraction, and more specifically by means of infomorphisms between different ways to (...)
  17. Formalising the 'No Information Without Data-Representation' Principle.Patrick Allo - 2008 - In P. Brey, A. Briggle & K. Waelbers (eds.), Current Issues in Computing and Philosophy. IOS Press.
    One of the basic principles of the general definition of information is its rejection of dataless information, which is reflected in its endorsement of an ontological neutrality. In general, this principles states that “there can be no information without physical implementation” (Floridi (2005)). Though this is standardly considered a commonsensical assumption, many questions arise with regard to its generalised application. In this paper a combined logic for data and information is elaborated, and specifically used to investigate the consequences of restricted (...)
  18. Vincent Hendricks, Mainstream and Formal Epistemology. [REVIEW]Patrick Allo - 2008 - Erkenntnis 69 (3):427-432.
    As Vincent Hendricks remarks early on in this book, the formal and mainstream traditions of epistemic theorising have mostly evolved independently of each other. This initial impression is confirmed by a comparison of the main problems and methods practitioners in each tradition are concerned with. Mainstream epistemol- ogy engages in a dialectical game of proposing and challenging definitions of knowledge. Formal epistemologists proceed differently, as they design a wide variety of axiomatic and model-theoretic methods whose consequences they investigate independently of (...)
  19. Local Information and Adaptive Consequence.Patrick Allo - 2006 - Logique Et Analyse 149:461-488.
    In this paper we provide a formal description of what it means to be in a local or partial information-state. Starting from the notion of locality in a relational structure, we define so-called adaptive gen- erated submodels. The latter are then shown to yield an adaptive logic wherein the derivability of Pφ is naturally interpreted as a core property of being in a state in which one holds the information that φ.
  20. Intuitionistic Autoepistemic Logic.Giambattista Amati, Luigia Carlucci-Aiello & Fiora Pirri - 1997 - Studia Logica 59 (1):103-120.
    In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.
  21. Toward a Logic of A Priori Knowledge.C. Anthony Anderson - 1993 - Philosophical Topics 21 (2):1-20.
  22. Revised Foundations for Imperative-Epistemic and Interrogative Logic.Lennart Aqvist - 1971 - Theoria 37 (1):33-73.
  23. A Logic for Information Systems.Dmitri A. Archangelsky & Mikhail A. Taitslin - 1997 - Studia Logica 58 (1):3-16.
    A conception of an information system has been introduced by Pawlak. The study has been continued in works of Pawlak and Orlowska and in works of Vakarelov. They had proposed some basic relations and had constructed a formal system of a modal logic that describes the relations and some of their Boolean combinations. Our work is devoted to a generalization of this approach. A class of relation systems and a complete calculus construction method for these systems are proposed. As a (...)
  24. Knowing and Supposing in Games of Perfect Information.Horacio Arló-Costa & Cristina Bicchieri - 2007 - Studia Logica 86 (3):353 - 373.
    The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we (...)
  25. Justification Logic.Sergei Artemov - forthcoming - Stanford Encyclopedia of Philosophy.
  26. The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
    We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...)
  27. Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
    In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...)
  28. On Propositional Quantifiers in Provability Logic.Sergei N. Artemov & Lev D. Beklemishev - 1993 - Notre Dame Journal of Formal Logic 34 (3):401-419.
  29. Finite Kripke Models and Predicate Logics of Provability.Sergei Artemov & Giorgie Dzhaparidze - 1990 - Journal of Symbolic Logic 55 (3):1090-1098.
    The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that $PA \nvdash fR$ . This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding "the predicate part" as a specific (...)
  30. The Basic Intuitionistic Logic of Proofs.Sergei Artemov & Rosalie Iemhoff - 2007 - Journal of Symbolic Logic 72 (2):439 - 451.
    The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.
  31. On First-Order Theories with Provability Operator.Sergei Artëmov & Franco Montagna - 1994 - Journal of Symbolic Logic 59 (4):1139-1153.
    In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable.
  32. Discovering Knowability: A Semantic Analysis.Sergei Artemov & Tudor Protopopescu - 2013 - Synthese 190 (16):3349-3376.
    In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...)
  33. Knowledge Means ‘All’, Belief Means ‘Most’.Dimitris Askounis, Costas D. Koutras & Yorgos Zikos - 2016 - Journal of Applied Non-Classical Logics 26 (3):173-192.
    We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion (...)
  34. DEL-Sequents for Progression.Guillaume Aucher - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):289-321.
    Dynamic Epistemic Logic (DEL) deals with the representation and the study in a multi-agent setting of knowledge and belief change. It can express in a uniform way epistemic statements about: 1. what is true about an initial situation 2. what is true about an event occurring in this situation 3. what is true about the resulting situation after the event has occurred. We axiomatize within the DEL framework what we can infer about (iii) given (i) and (ii). Given three formulas (...)
  35. An Internal Version of Epistemic Logic.Guillaume Aucher - 2010 - Studia Logica 94 (1):1-22.
    Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying the types of modeling points of view which are logically possible. We call the one traditionally followed by epistemic logic the perfect external approach, because there the modeler is assumed to be an omniscient and external observer of the epistemic situation. In the rest of the paper we focus on what we call the internal approach, where the modeler is (...)
  36. Knowledge in Flux: Modelling the Dynamics of Epistemic States.F. Jose Diez Ausín - 1990 - Theoria 5 (1):276-282.
  37. Peter GÄRDENFORS: Knowledge in Flux. Modelling the Dynamics of Epistemic States.F. José DÍez AusÍn - 1990 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 5 (12/13):276-282.
  38. Inductive Reasoning a Study of Tarka and its Role in Indian Logic.S. Bagchi - 1953 - Calcutta Oriental Press.
  39. 'Knowable' as 'Known After an Announcement'.Philippe Balbiani, Alexandru Baltag, Hans van Ditmarsch, Andreas Herzig, Tomohiro Hoshi & Tiago de Lima - 2008 - Review of Symbolic Logic 1 (3):305-334.
    Public announcement logic is an extension of multiagent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: after which , does it hold that Kφ? We give various semantic results and show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.
  40. The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence.Alexandru Baltag, Bryan Renne & Sonja Smets - 2014 - Annals of Pure and Applied Logic 165 (1):49-81.
    We present a complete, decidable logic for reasoning about a notion of completely trustworthy evidence and its relations to justifiable belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness (...)
  41. Completeness of Public Announcement Logic in Topological Spaces.C. A. N. Baskent - 2011 - Bulletin of Symbolic Logic 17 (1):142.
  42. The Need for Adaptative Logics in Epistemology.Diderik Batens - 2004 - In Shadid Rahman, John Symons, Dov Gabbay & Jean Bendegem (eds.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publishers. pp. 459-485.
  43. Review: Nicholas Rescher: Cognitive Harmony: The Role of Systematic Harmony in the Constitution of Knowledge; Epistemic Logic: A Survey of the Logic of Knowledge; and Realism and Pragmatic Epistemology. [REVIEW]H. Battaly - 2008 - Mind 117 (465):205-210.
  44. On Interactive Knowledge with Bounded Communication.Ido Ben-Zvi & Yoram Moses - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):323-354.
    The effect of upper bounds on message delivery times in a computer network upon the dynamics of knowledge gain is investigated. Recent work has identified centipedes and brooms?causal structures that combine message chains with time bound information?as necessary conditions for knowledge gain and common knowledge gain, respectively. This paper shows that, under the full-information protocol, these structures are both necessary and sufficient for such epistemic gain. We then apply this analysis to gain insights into the relation between ?everyone knows? and (...)
  45. The Dynamics of Awareness.Benthem Johan van & R. Velázquez-Quesada Fernando - 2010 - Synthese 177 (S1):5 - 27.
    Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents based on semantic information. The latter is produced by acts of observation or communication that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference— and key axioms of the system merely postulate "deductive closure". In this paper, we take the view that all information is produced by acts, and hence (...)
  46. Diversity of Logical Agents in Games.Johan van Benthem & Liu - 2004 - Philosophia Scientiae 8 (2):163-178.
    Epistemic agents may have different powers of observation and reasoning, and we show how this diversity fits into dynamic update logics.RésuméLes agents épistémiques peuvent avoir différents pouvoirs d’observation et de raisonnement, et nous montrons comment cette diversité prend place en logique dynamique de mise à jour.
  47. Toward a Dynamic Logic of Questions.Johan Benthem & Ştefan Minică - 2012 - Journal of Philosophical Logic 41 (4):633 - 669.
    Questions are triggers for explicit events of 'issue management'. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multiagent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.
  48. Lotteries and Prefaces.Matthew A. Benton - 2017 - In Jonathan Jenkins Ichikawa (ed.), The Routledge Handbook of Epistemic Contextualism. New York: Routledge. pp. 168-176.
    The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...)
  49. Simple Hyperintensional Belief Revision.F. Berto - 2018 - Erkenntnis:1-17.
    I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting to (...)
  50. On Conceiving the Inconsistent.Francesco Berto - 2014 - Proceedings of the Aristotelian Society 114 (1pt1):103-121.
    I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus counterfactual (...)
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