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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, 19521962. 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. Thomas Ågotnes & Hans van Ditmarsch (2011). What Will They Say?—Public Announcement Games. 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 (...)
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  2. Thomas Ågotnes & Hans van Ditmarsch (2011). What Will They Say?—Public Announcement Games. Synthese 179 (1):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 (...)
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  3. Guillaume Aucher (2011). DEL-Sequents for Progression. 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 (...)
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  4. Philippe Balbiani, Alexandru Baltag, Hans van Ditmarsch, Andreas Herzig, Tomohiro Hoshi & Tiago de Lima (2008). Knowable' as 'Known After an Announcement. 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.
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  5. Ido Ben-Zvi & Yoram Moses (2011). On Interactive Knowledge with Bounded Communication. 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 (...)
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  6. Johan Benthem & Ştefan Minică (2012). Toward a Dynamic Logic of Questions. 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.
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  7. Alexander Bochman (2001). A Logical Theory of Nonmonotonic Inference and Belief Change. Springer.
    This is the first book that integrates nonmonotonic reasoning and belief change into a single framework from an artificial intelligence logic point-of-view.
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  8. Michel Bourdeau (2003). Logic of Existence and Logic of Knowledge. Epistemic and Non Epistemic Aspects of Logic. Philosophia Scientiae 7 (2):147-163.
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  9. Gerhard Brewka, Jurgen Dix & Kurt Konolige (1997). Nonmonotonic Reasoning: An Overview. Center for the Study of Language and Inf.
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  10. Ivano A. Ciardelli & Floris Roelofsen (forthcoming). Inquisitive Dynamic Epistemic Logic. Synthese:1-45.
    Information exchange can be seen as a dynamic process of raising and resolving issues. The goal of this paper is to provide a logical framework to model and reason about this process. We develop an inquisitive dynamic epistemic logic (IDEL), which enriches the standard framework of dynamic epistemic logic (DEL), incorporating insights from recent work on inquisitive semantics. At a static level, IDEL does not only allow us to model the information available to a set of agents, like standard epistemic (...)
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  11. Peter Clark (1990). Nonmonotonic Reasoning , Argumentation and Machine Learning 1 Introduction. Argumentation:1-11.
    Machine learning and nonmonotonic reasoning are closely related, both concerned with making plausible as well as certain inferences based on available data. In this document a brief overview of different approaches to nonmonotonic reasoning is presented, and it is shown how the concept of argumentation systems arises. The relationship with machine learning work is also discussed. The document aims to highlight the links between nonmonotonic reasoning, argumentation and machine learning and as a result propose some potentially useful directions for new (...)
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  12. John Corcoran (1994). The Founding of Logic. Ancient Philosophy 14 (1):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
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  13. Roberta Corvi (2012). From Opinion to Knowledge: Epistemic Dynamic. Rivista di Filosofia Neo-Scolastica 104 (4):707-723.
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  14. Eleonora Cresto (2012). A Defense of Temperate Epistemic Transparency. Journal of Philosophical Logic 41 (6):923-955.
    Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...)
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  15. Maria Luisa Dalla Chiara (1991). Epistemic Logic Without Logical Omniscience. In Georg Schurz (ed.), Advances in Scientific Philosophy. 87.
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  16. Francien Dechesne & Yanjing Wang (2010). To Know or Not to Know: Epistemic Approaches to Security Protocol Verification. Synthese 177 (Supplement-1):51-76.
    Security properties naturally combine temporal aspects of protocols with aspects of knowledge of the agents. Since BAN-logic, there have been several initiatives and attempts to incorpórate epistemics into the analysis of security protocols. In this paper, we give an overview of work in the field and present it in a unified perspective, with comparisons on technical subtleties that have been employed in different approaches. Also, we study to which degree the use of epistemics is essential for the analysis of security (...)
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  17. Cédric Dégremont & Oliver Roy (2012). Agreement Theorems in Dynamic-Epistemic Logic. Journal of Philosophical Logic 41 (4):735-764.
    This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement (...)
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  18. Lorenz Demey (2013). Contemporary Epistemic Logic and the Lockean Thesis. Foundations of Science 18 (4):599-610.
    This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...)
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  19. Lorenz Demey (2012). Structures of Oppositions in Public Announcement Logic. In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. 313--339.
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  20. P. Egre (2007). VF Hendricks. Mainstream and Formal Epistemology. Bulletin of Symbolic Logic 13 (1).
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  21. Tuan-Fang Fan, I. -Peng Lin & Churn-Jung Liau (1997). Nonmonotonic Reasoning Based on Incomplete Logic. Journal of Applied Non-Classical Logics 7 (4):375-395.
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  22. Branden Fitelson (2003). Review of I. Hacking, An Introduction to Probability and Inductive Logic. [REVIEW] Bulletin of Symbolic Logic 9 (4):5006-5008.
  23. Andrés Cordón Franco, Hans van Ditmarsch & Angel Nepomuceno (2013). Dynamic Consequence and Public Announcement. Review of Symbolic Logic 6 (4):659-679.
    In van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as \$${\psi _1}, \ldots ,{\psi _n}{ \models ^d}\phi \,{\rm{iff}}{ \models ^{pa}}[{\psi _1}] \ldots [{\psi _n}]\phi ,\$$ where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation \$$models _{\rm{\Gamma }}^\$$ extending van Benthem, inspired by Makinson (2003) wherein Makinson calls this reasoning a set Γ. In the presence of common knowledge, conditional dynamic (...)
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  24. Andrés Cordón Franco, Hans van Ditmarsch & Angel Nepomuceno (2013). Dynamic Consequence and Public Announcement. Review of Symbolic Logic 6 (4):659-679.
    In van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as \$$\psi _1}, \ldots ,{\psi _n}{ \models ^d}\phi \,{\rm{iff}}{ \models ^{pa}}[{\psi _1}] \ldots [{\psi _n}]\phi \$$ where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation \$$models _{\rm{\Gamma }}^\$$ extending van Benthem, inspired by Makinson (2003) wherein Makinson calls this reasoning a set Γ. In the presence of common knowledge, conditional dynamic (...)
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  25. P. T. Geach (1963). Knowledge and Belief: An Introduction to the Logic of the Two Notions. Philosophical Books 4 (2):7-8.
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  26. Johan van Benthem Jelle Gerbrandy, Merging Frameworks for Interaction.
    Many logical systems today describe intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al. [8]), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam [22]), STIT (Belnap et al. [5]), Process Algebra and Game Semantics (Abramsky [1]). This variety is an asset, as different modeling tools can be fine-tuned to specific applications. But it may also be an obstacle, when barriers between paradigms and schools go up. This paper takes a closer look at one particular interface, between two systems (...)
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  27. R. Girle (1973). Epistemic Logic; Language and Concepts. Logique Et Analyse 63 (63):64.
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  28. Paul Gochet & Eric Gillet (1991). On Professor Weingartner's Contribution to Epistemic Logic. In Georg Schurz (ed.), Advances in Scientific Philosophy. 24--97.
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  29. V. F. Hendricks & Paul Egre (2007). REVIEWS-Mainstream and Format Epistemology. Bulletin of Symbolic Logic 13 (1).
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  30. Vincent F. Hendricks (2003). Active Agents. Journal of Logic, Language and Information 12 (4):469-495.
    The purpose of this survey is twofold: (1) to place some centralthemes of epistemic logic in a general epistemological context,and (2) to outline a new framework for epistemic logic developedjointly with S. Andur Pedersen unifying some key ``mainstream''epistemological concerns with the ``formal'' epistemologicalapparatus.
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  31. Frank Hofmann (2005). Epistemic Means and Ends: In Defense of Some Sartwellian Insights. Synthese 146 (3):357 - 369.
    The question of what means-and-ends structure our epistemic endeavors have is an important issue in recent epistemology, and is fundamental for understanding epistemic matters in principle. Crispin Sartwell has proposed arguments for the view that knowledge is our only ultimate goal, and justification is no part of it. An important argument is his instrumentality argument which is concerned with the conditions under which something could belong to our ultimate epistemic goal. Recently, this argument has been reconstructed and criticized by Pierre (...)
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  32. Tomohiro Hoshi & Eric Pacuit (2010). Dynamic Logics of Knowledge and Access. Synthese 177 (1):29 - 49.
    A recurring issue in any formal model representing agents' (changing) informational attitudes is how to account for the fact that the agents are limited in their access to the available inference steps, possible observations and available messages. This may be because the agents are not logically omniscient and so do not have unlimited reasoning ability. But it can also be because the agents are following a predefined protocol that explicitly limits statements available for observation and/or communication. Within the broad literature (...)
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  33. Hykel Hosni (2006). Makinson David. Bridges From Classical to Nonmonotonic Logic. Text in Computing, Vol. 5. King's College, London, 2005, Xvi+ 216 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (3):499-502.
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  34. C. Howson (1984). Review: Richard Jeffrey, Studies in Inductive Logic and Probability; , A Basic System of Inductive Logic, Part II. [REVIEW] Journal of Symbolic Logic 49 (4):1409-1410.
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  35. Lloyd Humberstone (2008). Invitation to Autoepistemology. Theoria 68 (1):13-51.
    The phrase ‘autoepistemic logic’ was introduced in Moore [1985] to refer to a study inspired in large part by criticisms in Stalnaker [1980] of a particular nonmonotonic logic proposed by McDermott and Doyle.1 Very informative discussions for those who have not encountered this area are provided by Moore [1988] and the wide-ranging survey article Konolige [1994], and the scant remarks in the present introductory section do not pretend to serve in place of those treatments as summaries of the field. A (...)
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  36. John T. Kearns (2005). Russell's Epistemic Understanding of Logic. Teorema: Revista Internacional de Filosofía 24 (3):115-132.
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  37. Charles F. Kielkopf (1972). A Note on Hintikka's Logic of Belief as an Ethics of Belief. Philosophical Studies 23 (1-2):135 - 137.
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  38. Louwe B. Kuijer (2013). The Expressivity of Factual Change in Dynamic Epistemic Logic. Review of Symbolic Logic 7 (2):1-14.
    A commonly used dynamic epistemic logic is one obtained by adding commonknowledge and public announcements to a basic epistemic logic. It is known from Kooi (2007) that adding public substitutions to such a logic adds expressivity over the class K of models. Here I show that substitutions also add expressivity over the classes KD45, S4 and S5 of models. Since the combination of common knowledge, public announcements and substitutions, was shown in Kooi (2007) to be equally expressive to relativized common (...)
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  39. Joohyung Lee, Vladimir Lifschitz & Hudson Turner, Nonmonotonic Causal Theories.
    cuted actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowl-.
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  40. Wolfgang Lenzen (1979). Epistemologische Betrachtungen Zu [S4, S5]. Erkenntnis 14 (1):33 - 56.
    The numerous modal systems between S4 and S5 are investigated from an epistemological point of view by interpreting necessity either as knowledge or as (strong) belief. It is shown that-granted some assumptions about epistemic logic for which the author has argued elsewhere-the system S4.4 may be interpreted as the logic of true belief, while S4.3.2 and S4.2 may be taken to represent epistemic logic systems for individuals who accept the scheme knowledge = true belief only for certain special instances. There (...)
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  41. Emiliano Lorini (2013). On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective Attitudes. [REVIEW] Journal of Philosophical Logic 42 (6):863-904.
    This paper proposes a logical framework for representing static and dynamic properties of different kinds of individual and collective attitudes. A complete axiomatization as well as a decidability result for the logic are given. The logic is applied to game theory by providing a formal analysis of the epistemic conditions of iterated deletion of weakly dominated strategies (IDWDS), or iterated weak dominance for short. The main difference between the analysis of the epistemic conditions of iterated weak dominance given in this (...)
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  42. P. Lukowski (2006). Epistemic Role of the Logic of Falsehood. Filozofia Nauki 14 (3 (55)):57-77.
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  43. John MacFarlane (2007). The Logic of Confusion: Remarks on Joseph Camp's Confusion: A Study in the Theory of Knowledge. Philosophy and Phenomenological Research 74:700-708.
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  44. Sébastien Magnier & Tiago De Lima, A Soundness & Completeness Proof on Dialogs and Dynamic Epistemic Logic.
    Since Plaza [1989], which is most of the time considered as the inaugural paper on announcement logics in public communication contexts, a lot of papers on dynamic epistemic logics have been published. The most famous dynamic epistemic logic is known by the name of PAL (Public Announcement Logic). The logic PAC is an extension of PAL with the common knowledge operator (CG). Soundness and completeness proofs of those logics are presented in van Ditmarsch et al. [2008], in Balbiani et al. (...)
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  45. Patrick Maher (2010). Explication of Inductive Probability. Journal of Philosophical Logic 39 (6):593 - 616.
    Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.
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  46. David Makinson (2009). Levels of Belief in Nonmonotonic Reasoning. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. 341--354.
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  47. David Makinson (1994). General Patterns in Nonmonotonic Reasoning. In Handbook of Logic in Artificial Intelligence Nad Logic Programming, Vol. Iii. Clarendon Press.
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  48. David Makinson & Peter Gärdenfors (1991). Relations Between the Logic of Theory Change and Nonmonotonic Logic. In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer. 183--205.
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  49. J. McClelland (1971). Epistemic Logic and the Paradox of the Surprise Examination. International Logic Review 3:69-85.
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  50. David Miller (1970). Review: Marguerite H. Foster, Michael L. Martin, Probability, Conformation, and Simplicity. Readings in the Philosophy of Inductive Logic. [REVIEW] Journal of Symbolic Logic 35 (3):451-454.
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