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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. F. Jose Diez Ausín (1990). Knowledge in Flux: Modelling the Dynamics of Epistemic States. Theoria 5 (1):276-282.
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  2. Johan Van Benthem (2006). Epistemic Logic and Epistemology: The State of Their Affairs. Philosophical Studies 128 (1):49 - 76.
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  3. Hans Van Ditmarsch & Willem Labuschagne (2007). My Beliefs About Your Beliefs: A Case Study in Theory of Mind and Epistemic Logic. Synthese 155 (2):191 - 209.
    We model three examples of beliefs that agents may have about other agents' beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs ('no preferences'), that agents believe that the beliefs of other agents are in part as their own ('my preferences'), and the special (...)
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  4. Jacques Dubucs (1991). On Logical Omniscience. Logique Et Analyse 133 (133-140):41-55.
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  5. R. Mclaughlin (1986). SCHLESINGER, G.: "The Range of Epistemic Logic". Australasian Journal of Philosophy 64:530.
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  6. 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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  7. W. Minto (1895). Logic Inductive and Deductive. Philosophical Review 4:342.
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  8. Krystyna Misiuna (2011). O pewnej logice informacji. Filozofia Nauki 1.
    The main aim of the present article is an outline of an intuitively adequate system of logic of the operator "being informed". Such a system should be different from the familiar systems of epistemic and doxastic logic. The principle of veracity occurring in epistemic logics does not describe adequately the information operator, since the information may be true as well as false. On the other hand, the principle of consistency of beliefs, occurring in doxastic logics, cannot be applied to information, (...)
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  9. Charles G. Morgan (2000). The Nature of Nonmonotonic Reasoning. Minds and Machines 10 (3):321-360.
    Conclusions reached using common sense reasoning from a set of premises are often subsequently revised when additional premises are added. Because we do not always accept previous conclusions in light of subsequent information, common sense reasoning is said to be nonmonotonic. But in the standard formal systems usually studied by logicians, if a conclusion follows from a set of premises, that same conclusion still follows no matter how the premise set is augmented; that is, the consequence relations of standard logics (...)
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  10. K. Nakamatsu & A. Suzuki (1995). On the Relation Between Nonmonotonic ATMS and ALPSN. Proc. Japanese Society for Ai Sig Fai 9502 (1):1-8.
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  11. Erik J. Olsson & David Westlund (2006). On the Role of the Research Agenda in Epistemic Change. Erkenntnis 65 (2):165 - 183.
    The standard way of representing an epistemic state in formal philosophy is in terms of a set of sentences, corresponding to the agent’s beliefs, and an ordering of those sentences, reflecting how well entrenched they are in the agent’s epistemic state. We argue that this wide-spread representational view – a view that we identify as a “Quinean dogma” – is incapable of making certain crucial distinctions. We propose, as a remedy, that any adequate representation of epistemic states must also include (...)
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  12. Ewa Orlowska (1989). Logic For Reasoning About Knowledge. Mathematical Logic Quarterly 35 (6):559-572.
    One of the important issues in research on knowledge based computer systems is development of methods for reasoning about knowledge. In the present paper semantics for knowledge operators is introduced. The underlying logic is developed with epistemic operators relative to indiscernibility. Facts about knowledge expressible in the logic are discussed, in particular common knowledge and joint knowledge of n group of agents. Some paradoxes of epistemic logic are shown to be eliminated in the given system. A formal logical analysis of (...)
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  13. Eric Pacuit (2013). Dynamic Epistemic Logic I: Modeling Knowledge and Belief. Philosophy Compass 8 (9):798-814.
    Dynamic epistemic logic, broadly conceived, is the study of logics of information change. This is the first paper in a two-part series introducing this research area. In this paper, I introduce the basic logical systems for reasoning about the knowledge and beliefs of a group of agents.
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  14. Eric Pacuit (2013). Dynamic Epistemic Logic II: Logics of Information Change. Philosophy Compass 8 (9):815-833.
    This is the second paper in a two-part series introducing logics for reasoning about the dynamics of knowledge and beliefs. Part I introduced different logical systems that can be used to reason about the knowledge and beliefs of a group of agents. In this second paper, I show how to adapt these logical systems to reason about the knowledge and beliefs of a group of agents during the course of a social interaction or rational inquiry. Inference, communication and observation are (...)
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  15. John Pais (1992). Faithful Representation of Nonmonotonic Patterns of Inference. Minds and Machines 2 (1):27-49.
    Recently, John Bell has proposed that a specific conditional logic, C, be considered as a serious candidate for formally representing and faithfully capturing various (possibly all) formalized notions of nonmonotonic inference. The purpose of the present paper is to develop evaluative criteria for critically assessing such claims. Inference patterns are described in terms of the presence or absence of residual classical monotonicity and intrinsic nonmonotonicity. The concept of a faithful representation is then developed for a formalism purported to encode a (...)
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  16. J. B. Paris & A. Vencovská (2012). Symmetry in Polyadic Inductive Logic. Journal of Logic, Language and Information 21 (2):189-216.
    A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.
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  17. Jeff B. Paris & Alena Vencovská (2011). A Note on Irrelevance in Inductive Logic. Journal of Philosophical Logic 40 (3):357 - 370.
    We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson's Sufficientness Principle, JSP, which is classically important because it leads to Carnap's influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix-Paris Continuum. We argue that the derivation of two very disparate families of inductive methods from alternative perceptions of (...)
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  18. Carlo Proietti & Erik J. Olsson (2014). A DDL Approach to Pluralistic Ignorance and Collective Belief. Journal of Philosophical Logic 43 (2-3):499-515.
    A group is in a state of pluralistic ignorance (PI) if, roughly speaking, every member of the group thinks that his or her belief or desire is different from the beliefs or desires of the other members of the group. PI has been invoked to explain many otherwise puzzling phenomena in social psychology. The main purpose of this article is to shed light on the nature of PI states – their structure, internal consistency and opacity – using the formal apparatus (...)
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  19. Wlodek Rabinowicz, Epistemic Logic: Questions and Answers.
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  20. Ana Rosa Pérez Ransanz (2011). El papel de las emociones en la producción de conocimiento. Estudios Filosóficos 60 (173):51-64.
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  21. Veikko Rantala (2006). Learning and Epistemic Logic. Acta Philosophica Fennica 78:139.
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  22. William J. Rapaport (1988). Review: Cynthia Dwork, Yoram Moses, Knowledge and Common Knowledge in a Byzantine Environment I: Crash Failures. [REVIEW] Journal of Symbolic Logic 53 (2):666-666.
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  23. Manuel Rebuschi (2006). IF and Epistemic Action Logic. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. 261--281.
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  24. Nicholas Rescher (2005). Epistemic Logic: A Survey of the Logic of Knowledge. University of Pittsburgh Press.
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  25. Jan-Willem Romeijn (2012). Conditioning and Interpretation Shifts. Studia Logica 100 (3):583-606.
    This paper develops a probabilistic model of belief change under interpretation shifts, in the context of a problem case from dynamic epistemic logic. Van Benthem [4] has shown that a particular kind of belief change, typical for dynamic epistemic logic, cannot be modelled by standard Bayesian conditioning. I argue that the problems described by van Benthem come about because the belief change alters the semantics in which the change is supposed to be modelled: the new information induces a shift in (...)
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  26. Katsuhiko Sano & Satoshi Tojo (2013). Dynamic Epistemic Logic for Channel-Based Agent Communication. In Kamal Lodaya (ed.), Logic and its Applications. Springer. 109--120.
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  27. Karl Schlechta (1997). Nonmonotonic Logics Basic Concepts, Results, and Techniques.
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  28. Renate A. Schmidt & Dmitry Tishkovsky (2008). On Combinations of Propositional Dynamic Logic and Doxastic Modal Logics. Journal of Logic, Language and Information 17 (1):109-129.
    We prove completeness and decidability results for a family of combinations of propositional dynamic logic and unimodal doxastic logics in which the modalities may interact. The kind of interactions we consider include three forms of commuting axioms, namely, axioms similar to the axiom of perfect recall and the axiom of no learning from temporal logic, and a Church–Rosser axiom. We investigate the influence of the substitution rule on the properties of these logics and propose a new semantics for the test (...)
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  29. Krister Segerberg (1997). A Doxastic Walk with Darwiche and Pearl. Nordic Journal of Philosophical Logic 2 (1):63-66.
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  30. Krister Segerberg (1995). Dynamic Logic. In Audi Robert (ed.), The Cambridge Dictionary of Philosophy. Cambridge University Press.
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  31. Sebastian Sequoiah-Grayson (2013). Epistemic Closure and Commutative, Nonassociative Residuated Structures. Synthese 190 (1):113-128.
    K-axiom-based epistemic closure for explicit knowledge is rejected for even the most trivial cases of deductive inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation. The recognition that deductive inference concerns interaction as much as it concerns consequence allows for perspectives from logics of multi-agent information flow to be refocused onto mono-agent deductive reasoning. Instead of modeling the information flow between different agents in a communicative or announcement setting, we model (...)
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  32. Ricardo Silvestre (2011). An Inductive Modal Approach for the Logic of Epistemic Inconsistency. Abstracta 6 (1):136-155.
    The purpose of this paper is twofold. First we want to extent a specific paranormal modal logic in such a way as obtain a paraconsistent and paracomplete multimodal logic able to formalize the notions of plausibility and certainty. With this logic at hand, and this is our second purpose, we shall use a modified version of Reiter‘s default logic to build a sort of inductive logic of plausibility and certainty able to represent some basic principles of epistemic inductive reasoning, such (...)
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  33. Ricardo Sousa Silvestre (2011). Induction and Confirmation Theory: An Approach Based on a Paraconsistent Nonmonotonic Logic. Princípios 17 (28):71-98.
    This paper is an effort to realize and explore the connections that exist between nonmonotonic logic and confirmation theory. We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense. By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of induction, having (...)
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  34. Roy Sorenson (1987). George N. Schlesinger, The Range of Epistemic Logic. [REVIEW] Philosophy in Review 7:81-83.
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  35. Roy A. Sorenson (1987). George N. Schlesinger, The Range of Epistemic Logic Reviewed By. Philosophy in Review 7 (2):81-83.
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  36. Zbigniew Stachniak (1995). Nonmonotonic Theories and Their Axiomatic Varieties. Journal of Logic, Language and Information 4 (4):317-334.
    The properties of monotonic inference systems and the properties of their theories are strongly linked. These links, however, are much weaker in nonmonotonic inference systems. In this paper we introduce the notion of anaxiomatic variety for a theory and show how this notion, instead of the notion of a theory, can be used for the syntactic and semantic analysis of nonmonotonic inferences.
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  37. Satoru Suzuki (2009). Prolegomena to Dynamic Epistemic Preference Logic. In Hattori (ed.), New Frontiers in Artificial Intelligence. Springer. 177--192.
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  38. Johan van Benthem (forthcoming). Epistemic Logic and Epistemology. The State of Their Affairs', to Appear in V. Hendricks, Ed., Special Issue Of. Philosophical Studies.
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  39. van Benthem, Johan, van Eijck, Jan & Kooi, Barteld, Logics of Communication and Change.
    Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also (...)
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  40. Johan van Benthem & Fernando R. Velázquez-Quesada (2010). The Dynamics of Awareness. Synthese 177 (1):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 we (...)
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  41. H. van Ditmarsch, W. van der Hoek & B. Kooi (2005). Playing Cards with Hintikka: An Introduction to Dynamic Epistemic Logic. Australasian Journal of Philosophy 3:108-134.
    This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the (...)
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  42. Hans van Ditmarsch, Andreas Herzig & Tiago De Lima (2012). Public Announcements, Public Assignments and the Complexity of Their Logic. Journal of Applied Non-Classical Logics 22 (3):249-273.
    We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations of subformulae (...)
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  43. Jan van Eijck, Modelling Epistemic Updates with Functional Programming.
    Epistemic logic is the logic of knowledge, and dynamic epistemic logic is the logic of effects of communicative actions on the knowledge states of a set of agents. Typical communicative actions are making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [3], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modelling tool (...)
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  44. Jan van Eijck, Modelling the Epistemics of Communication with Functional Programming.
    Dynamic epistemic logic is the logic of the effects of epistemic actions like making public announcements, passing private messages, revealing secrets, telling lies. This paper takes its starting point from the version of dynamic epistemic logic of [2], and demonstrates a tool that can be used for showing what goes on during a series of epistemic updates: the dynamic epistemic modelling tool DEMO [7, 9]. DEMO allows modelling epistemic updates, graphical display of update results, graphical display of action models, formula (...)
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  45. Yanjing Wang & Qinxiang Cao (2013). On Axiomatizations of Public Announcement Logic. Synthese (S1):1-32.
    In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the (...)
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  46. Frank Wolter & Michael Wooldridge (2012). Temporal and Dynamic Logic. Journal of the Indian Council of Philosophical Research 1.
    We present an introductory survey of temporal and dynamic logics: logics for reasoning about how environments change over time, and how dynamic processes affect their environments.We begin by introducing the historical development of temporal and dynamic logic, starting with the seminal work of Prior. This leads to a discussion of the use of temporal and dynamic logic in computer science. We describe LTL, CTL, and PDL; three key formalisms used in computer science for reasoning about programs, and illustrate how these (...)
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  47. Audrey Yap (2014). Idealization, Epistemic Logic, and Epistemology. Synthese 191 (14):3351-3366.
    Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating it as descriptive matches the (...)
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  48. Paul Ziff (1950). Review: W. H. Werkmeister, The Basis and Structure of Knowledge. [REVIEW] Journal of Symbolic Logic 15 (1):74-74.
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  49. Piotr Łukowski (2013). Is Human Reasoning Really Nonmonotonic? Logic and Logical Philosophy 22 (1):63-73.
    It seems that nonmonotonicity of our reasoning is an obvious truth. Almost every logician not even believes, but simply knows very well that a human being thinks in a nonmonotonic way. Moreover, a nonmonotonicity of thinking seems to be a phenomenon parallel to the existence of human beings. Examples allegedly illustrating this phenomenon are not even analyzed today. They are simply quoted. Nowadays, this is a standard approach to nonmonotonicity. However, even simple analysis of those “obvious” examples shows that they (...)
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Doxastic and Epistemic Logic
  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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