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Logics of Rational Interaction

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Dynamic Formal Epistemology

Part of the book series: Synthese Library ((SYLI,volume 351))

Abstract

This paper provides an overview of temporal and dynamic epistemic logic, two important logical approaches to rational interaction. There are may approaches to rational interaction and a natural question is how the approaches under consideration are related. We will also discuss relations to other logics and applications.

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Notes

  1. 1.

    The interested reader can consult Meyer and Veltman (2007), van der Hoek and Wooldridge (2003), van Benthem (2008a) and references therein.

  2. 2.

    A Kripke structure is a set of states with relations on this set for each agent. The states, or possible worlds, represent different ways the social situation could have evolved and the relations describe the agents’ (current) information. See, for example, Fagin et al. (1995) for details.

  3. 3.

    Of course, this is not meant to be a complete analysis of “social politeness”.

  4. 4.

    There is a large literature addressing the many subtleties surrounding the very notion of an event and when one event causes another event (see, for example, Cartwright 2007). However, for this chapter we take the notion of event as primitive. What is needed is that if an event takes place at some time t, then the fact that the event took place can be observed by a relevant set of agents at t. Compare this with the notion of an event from probability theory . If we assume that at each clock tick a coin is flipped exactly once, then “the coin landed heads” is a possible event. However, “the coin landed heads more than tails” would not be an event, since it cannot be observed at any one moment. As we will see, the second statement will be considered a property of histories, or sequences of events .

  5. 5.

    To be precise, elements of Σ should, perhaps, be thought of as event types whereas elements of a history are event tokens.

  6. 6.

    Although we will not do so here, typically it is assumed that ~ i is an equivalence relation.

  7. 7.

    As opposed to soft information which may be revised. See van Benthem (2007) for a general discussion of hard and soft information.

  8. 8.

    Note that we do not include any reflexive arrows in the picture in order to keep things simple.

  9. 9.

    This may be different from what the agent does observe in a given situation.

  10. 10.

    Again, the R i are often taken to be equivalence relations on W – but we do not commit.

  11. 11.

    Of course, we must assume that she knows precisely when Charles will meet with Bob.

  12. 12.

    The first formal connection was established by Gerbrandy (1999a, Section 5.3).

  13. 13.

    The preconditions of DEL also encode protocol information of a “local” character, and hence they can do some of the work of global protocols, as has been pointed out by van Benthem (2006).

  14. 14.

    Interestingly, van der Meyden (1994) showed in languages with an “until” operator (\(\varphi U\psi\) meaning there is a point in the future satisfying ψ and that ϕ is true at every moment until that point) adding only this axiom to an epistemic and temporal logic is not complete for ETL frames with perfect recall. What is needed is the more complex axiom scheme: \(K_i\varphi_1\wedge N(K_i\varphi_2\wedge\neg K_i\varphi_3)\rightarrow L_i((K_i\varphi_1)\ U[(K_i\varphi_2)U\neg\varphi_3])\), where “N” is the next-time operator – after any event e (cf. Halpern et al. 2004).

  15. 15.

    In fact, they show that the validity problem for public announcement logic with iteration is highly undecidable (\(\varPi_1^1\)-complete). In light of the translation between the DEL framework and the ETL framework discussed in Section 2.2.3, this is related to classic results of Halpern and Vardi (1989) showing that the validity problem for ETL frames that satisfy perfect recall and no miracles in certain modal languages is \(\varPi_1^1\)-complete. See van Benthem et al. (2009, Section 6.1) for an extended discussion of this relationship.

  16. 16.

    Closely related are the dynamic logics of preferences discussed by van Benthem and Liu (2007) .

  17. 17.

    Both Reiter (2001) and McCarthy and Hayes (1969) discuss this classic problem of AI.

  18. 18.

    Regrettably the English translations we consulted do not contain this phenomenon.

  19. 19.

    That is, situations in which the structure of the game is not common knowledge . For example, games where players may be uncertain about their own available actions and preferences and/or the available actions and preferences of the other players . This should be contrasted with imperfect information games where players may receive different information during the course of the game. See Myerson (2004) for a recent discussion of Harsanyi’s classic paper.

  20. 20.

    Typically this means the players first-order beliefs about the available choices of the other players, the players beliefs about the other players beliefs about these first-order beliefs , and so on ad infinitum.

  21. 21.

    Or, in the case of a one-shot strategic game , whether such statements can be revised during the players’ initial period of deliberation.

References

  • Ågotnes T, Alechina N (2007) The dynamics of syntactic knowledge. Journal of Logic and Computation 17(1):83–116

    Article  Google Scholar 

  • Alchourrón C, Gärdenfors P, Makinson D (1985) On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50:510–530

    Article  Google Scholar 

  • Alechina N, Logan B, Nguyen HN, Rakibl A (2009) Verifying time, memory and communication bounds in systems of reasoning agents. Synthese (Knowledge, Rationality & Action) 169(2):385–403

    Google Scholar 

  • Artemov S, Nogina E (2005) Introducing justification into epistemic logic. Journal of Logic and Computation 15(6):1059–1073

    Article  Google Scholar 

  • Aucher G (2003) A combined system for update logic and belief revision. Master’s thesis, ILLC, University of Amsterdam, Amsterdam

    Google Scholar 

  • Aucher G (2007) Interpreting an action from what we perceive and what we expect. Journal of Applied Non-Classical Logics 17(1):9–38

    Article  Google Scholar 

  • Aucher G, Herzig A (2007a) From DEL to EDL: exploring the power of converse events. In: Mellouli K (ed) Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2007), Springer Verlag Berlin, LNCS, vol 4724, pp 199–209, ftp://ftp.irit.fr/IRIT/LILAC/Ecsqaru2007.pdf

    Chapter  Google Scholar 

  • Aumann R (1976) Agreeing to disagree. Annals of Statistics 4:1236–1239

    Article  Google Scholar 

  • Aumann R (1999) Interactive epistemology I: Knowledge. International Journal of Game Theory 28:263–300

    Article  Google Scholar 

  • Balbiani P, Baltag A, van Ditmarsch H, Herzig A, Hoshi T, de Lima T (2007) What can we achieve by arbitrary announcements? – A dynamic take on Fitch’s knowability. In: Samet D (ed) Proceedings of TARK 2007, pp 42–51

    Google Scholar 

  • Baltag A (2002) A logic for suspicious players: epistemic actions and belief-updates in games. Bulletin of Economic Research 54(1):1–45

    Article  Google Scholar 

  • Baltag A, Moss LS (2004) Logics for epistemic programs. Synthese 139(2):165–224

    Article  Google Scholar 

  • Baltag A, Smets S (2008a) A qualitative theory of dynamic interactive belief revision. In: Bonanno G, van der Hoek W, Wooldridge M (eds) Proceedings of LOFT 2007, Amsterdam University Press, Amsterdam, Texts in Logic and Games, vol 3, pp 9–58

    Google Scholar 

  • Baltag A, Moss L, Solecki S (1998a) The logic of public announcements, common knowledge and private suspicions. In: Gilboa I (ed) Proceedings TARK 1998, Morgan Kaufmann Publishers Inc., pp 43–56

    Google Scholar 

  • Baltag A, Moss L, Solecki S (1998b) The logic of public announcements, common knowledge, and private suspicions. In: Gilboa I (ed) Proceedings of the 7th conference on Theoretical aspects of rationality and knowledge, Morgan Kaufmann Publishers Inc., p 56

    Google Scholar 

  • van Benthem J (1989) Semantic parallels in natural language and computation. In: Ebbinghaus HD, Fernandez-Prida J, Garrido M, Lascar D, Artalejo MR (eds) Logic Colloquium ’87, North-Holland, Amsterdam

    Google Scholar 

  • van Benthem J (2001) Games in dynamic-epistemic logic. Bulletin of Economic Research 53(4):219–248

    Article  Google Scholar 

  • van Benthem J (2003) Conditional probability meets update logic. Journal of Logic, Language and Information 12(4):409–421

    Article  Google Scholar 

  • van Benthem J (2004) What one may come to know. Analysis 64(2):95–105

    Article  Google Scholar 

  • van Benthem J (2005) Rational animals: What is ‘KRA’?, http://staff.science.uva.nl/johan/publications.html, invited lecture Malaga ESSLLI Summer School 2006

  • van Benthem J (2006) One is a lonely number: on the logic of communication. In: Chatzidakis Z, Koepke P, Pohlers W (eds) Logic Colloquium’02, Lecture Notes in Logic ASL & A.K. Peters, Wellesley, pp 96–129, Tech. Rep. PP-2003-07, ILLC, Amsterdam (2002)

    Google Scholar 

  • van Benthem J (2007) Dynamic logic for belief revision. Journal of Applied Non-Classical Logics 17(2):129–155

    Article  Google Scholar 

  • van Benthem J (2008a) Logical dynamics of information and interaction. Book manuscript

    Google Scholar 

  • van Benthem J (2008b) Merging observation and access in dynamic logic. Manuscript

    Google Scholar 

  • van Benthem J (2010) Logical dynamics of information and interaction. ILLC Manuscript, to appear with Cambridge University Press

    Google Scholar 

  • van Benthem J, Dégremont C (2009) Building bridges between dynamic and temporal doxastic logics. In: Proceedings of LOFT 8

    Google Scholar 

  • van Benthem J, Ikegami D (2008) Modal fixed-point logic and changing models. In: Avron A, Dershowitz N, Rabinovich A (eds) Pillars of computer science, essays dedicated to Boris (Boaz) Trakhtenbrot on the occasion of his 85th birthday, LNCS, vol 4800, Springer-Verlag, Berlin, pp 146–165

    Google Scholar 

  • van Benthem J, Liu F (2007) Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2):157–182

    Article  Google Scholar 

  • van Benthem J, Pacuit E (2006) The tree of knowledge in action: Towards a common perspective. In: Governatori G, Hodkinson I, Venema Y (eds) Advances in modal logic volume 6, King’s College Press, London pp 87–106

    Google Scholar 

  • van Benthem J, van Eijck J, Kooi B (2006) Logics of communication and change. Information and Computation 204(11):1620–1662

    Article  Google Scholar 

  • van Benthem J, Gerbrandy J, Hoshi T, Pacuit E (2009a) Merging frameworks of interaction. Journal of Philosophical Logic 38:491–526

    Article  Google Scholar 

  • van Benthem J, Gerbrandy J, Kooi B (2009b) Dynamic update with probabilities. Studia Logica 93(1):67–96

    Article  Google Scholar 

  • Blackburn P, de Rijke M, Venema Y (2002) Modal logic. Cambridge University Press, Cambridge

    Google Scholar 

  • Bleeker A, van Eijck J (2000) The epistemics of encryption. Tech. Rep. INS-R0019, CWI, Amsterdam, available from http://db.cwi.nl/rapporten/

  • Bonanno G (2004) Memory and perfect recall in extensive games. Games and Economic Behaviour 47:237–256

    Article  Google Scholar 

  • Bonanno G (2007) Axiomatic characterization of AGM belief revision in a temporal logic. Artificial Intelligence 171:144–160

    Article  Google Scholar 

  • Bonanno G, Battigalli P (1999) Recent results on belief, knowledge and the epistemic foundations of game theory. Research in Economics 53(2):149–225

    Article  Google Scholar 

  • Brandenburger A (2007) The power of paradox: some recent developments in interactive epistemology. International Journal of Game Theory 35:465–492

    Article  Google Scholar 

  • Bratman M (1987) Intention, plans and practical reason. Harvard University Press, London

    Google Scholar 

  • Bratman M (2007) Structures of agency. Oxford University Press, Oxford

    Google Scholar 

  • Cantwell J (2006) A formal model of multi-agent belief-interaction. Journal of Logic, Language and Information 15(4):303–329

    Article  Google Scholar 

  • Cartwright N (2007) Hunting causes and using them: Approaches in philosophy and economics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Dechesne F, Wang Y (2007) Dynamic epistemic verification of security protocols: framework and case study. In: van Benthem J, Ju S, Veltman F (eds) A meeting of the minds, Proceedings of the Workshop on Logic, Rationality and Interaction, Beijing, 2007, College Publications, London, Texts in Computer Science, vol 8, pp 129–143

    Google Scholar 

  • van Ditmarsch H, Kooi B (2008) Semantic results for ontic and epistemic change. In: Bonanno G, van der Hoek W, Wooldridge M (eds) Logic and the foundations of game and decision theory. Amsterdam University Press, Amsterdam, pp 87–117

    Google Scholar 

  • van Ditmarsch H, van der Hoek W, Kooi B (2007) Dynamic epistemic logic. Synthese library, Springer, New York

    Google Scholar 

  • van Ditmarsch HP (2003) The Russian cards problem. Studia Logica 75:31–62

    Article  Google Scholar 

  • van Ditmarsch HP (2005) Prolegomena to dynamic logic for belief revision. Synthese (Knowledge, Rationality & Action) 147:229–275

    Google Scholar 

  • van Ditmarsch HP, Kooi B (2006) The secret of my success. Synthese 151(2):201–232

    Article  Google Scholar 

  • van Ditmarsch HP, van der Hoek W, Kooi BP (2005) Dynamic epistemic logic with assignment. In: Dignum F, Dignum V, Koenig S, Kraus S, Singh MP, Wooldridge M (eds) Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 05), ACM Inc, New York, vol 1, pp 141–148

    Chapter  Google Scholar 

  • van Ditmarsch HP, van der Hoek W, van der Meyden R, Ruan J (2006) Model checking russian cards. Electronic Notes in Theoretical Computer Science 149:790–795

    Google Scholar 

  • Duc HN (1997) Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 7(5):633–648

    Article  Google Scholar 

  • Duc HN (2001) Resource-bounded reasoning about knowledge. PhD thesis, Universität Leipzig

    Google Scholar 

  • van Eijck J (2004a) Guarded actions. Tech. Rep. SEN-E0425, CWI, Amsterdam, available from http://db.cwi.nl/rapporten/

  • van Eijck J (2004b) Reducing dynamic epistemic logic to PDL by program transformation. Tech. Rep. SEN-E0423, CWI, Amsterdam, available from http://db.cwi.nl/rapporten/

  • van Eijck J (2005) DEMO: a system for dynamic epistemic modeling. http://homepages.cwi.nl/jve/demo

  • van Eijck J, Orzan SM (2005) Modelling the epistemics of communication with functional programming. In: van Eekelen M (ed) Sixth Symposium on Trends in Functional Programming TFP’05, pp 44–59

    Google Scholar 

  • Fagin R, Halpern J, Moses Y, Vardi M (1995) Reasoning about knowledge. The MIT Press, Boston

    Google Scholar 

  • de Finetti B (1937) La prevision: Ses lois logiques, ses sources subjectives. In: Annales de l’Institut Henri Poincare 7, Paris, pp 1–68, translated into English by Henry E. Kyburg Jr., Foresight: Its logical laws, its subjective sources. In Henry E. Kyburg Jr. and Howard E. Smokler (1964, eds), Studies in subjective probability, 53–118, Wiley, New York

    Google Scholar 

  • Fitting M (2009) Reasoning with justifications. In: Makinson D, Malinowski J, Wansing H (eds) Towards mathematical philosophy, trends in logic, vol 28, Springer, Dordrecht, Netherlands, pp 107–123

    Google Scholar 

  • French T, van der Meyden R, Reynolds M (2004) Axioms for logics of knowledge and past time: Synchrony and unique initial states. In: Advances in Modal Logic, pp 53–72

    Google Scholar 

  • Friedman N, Halpern J (1997) Modeling belief in dynamic systems. Part I: Foundations. Artificial Intelligence 95(2):257–316

    Article  Google Scholar 

  • Friedman N, Halpern J (1999) Modeling belief in dynamic systems. Part II: Revision and update. Journal of AI Research 10:117–167

    Google Scholar 

  • Gerbrandy J (1999a) Bisimulations on planet kripke. PhD thesis, Institute for Logic, Language and Computation (DS-1999-01)

    Google Scholar 

  • Gerbrandy J, Groeneveld W (1997) Reasoning about information change. Journal of Logic, Language and Information 6(2):147–169

    Article  Google Scholar 

  • Gerbrandy JD (2007) The surprise examination in dynamic epistemic logic. Synthese 155(1):21–33

    Article  Google Scholar 

  • Grimm J, Grimm W (1857) Kinder- und Hausmärchen. Göttingen

    Google Scholar 

  • Halpern J (1999) Set-theoretic completeness for epistemic and conditional logic. Annals of Mathematics and Artificial Intelligence 26:1–27

    Article  Google Scholar 

  • Halpern J, Pucella R (2003) Modeling adversaries in a logic for security protocol analysis. In: Formal Aspects of Security

    Google Scholar 

  • Halpern J, Vardi M (1989) The complexity of reasoning about knowledge and time. Journal of Computer and System Sciences 38:195–237

    Article  Google Scholar 

  • Halpern J, van der Meyden R, Vardi M (2004) Complete axiomatizations for reasoning about knowledge and time. SIAM Journal of Computing 33(2):674–703

    Article  Google Scholar 

  • Halpern J (2003) Reasoning about Uncertainty. The MIT Press, Cambridge, MA

    Google Scholar 

  • Harsanyi J (1967) Games with incomplete informations played by ‘bayesian’ players. Management Science 14:159–182, 320–334, 486–502

    Article  Google Scholar 

  • Herzig A, de Lima T (2006) Epistemic actions and ontic actions: a unified logical framework. In: Simão Sichman J, Coelho H, Oliveira Rezende S (eds) Advances in Artificial Intelligence – IBERAMIA-SBIA 2006, Springer-Verlag, Berlin, Lecture Notes in Computer Science, vol 4140, pp 409–418

    Chapter  Google Scholar 

  • Herzig A, Lang J, Polacsek T (2000b) A modal logic for epistemic tests. In: Horn W (ed) Proceedings of ECAI 2000, pp 553–557

    Google Scholar 

  • Hodkinson I, Reynolds M (2006) Temporal logic. In: Blackburn P, van Benthem J, Wolter F (eds) Handbook of modal logic, studies in logic, vol 3, Elsevier, Amsterdam, pp 655–720

    Google Scholar 

  • van der Hoek W, Pauly M (2006) Modal logic for games and information. In: Blackburn P, van Benthem J, Wolter F (eds) Handbook of modal logic, studies in logic, vol 3, Elsevier, Amsterdam pp 1077–1148

    Google Scholar 

  • van der Hoek W, Wooldridge M (2003) Towards a logic of rational agency. Logic Journal of the IGPL 11(2):135–160

    Article  Google Scholar 

  • Hommersom A, Meyer JJC, de Vink E (2004) Update semantics of security protocols. Synthese (Knowledge, Rationality & Action) 142:229–267

    Google Scholar 

  • Horty J (2001a) Agency and deontic logic. Oxford University Press, Oxford

    Book  Google Scholar 

  • Hoshi T, Yap A (2009) Dynamic epistemic logic with branching temporal structures. Synthese (Knowledge, Rationality & Action)

    Google Scholar 

  • Hyman J, Steward H (eds) (2004) Agency and action. Cambridge University Press, Cambridge

    Google Scholar 

  • Jago M (2006) Logics for resource-bounded agents. PhD thesis, University of Nottingham

    Google Scholar 

  • Kooi B (2003a) Knowledge, chance, and change. PhD thesis, University of Groningen, iLLC Dissertation Series DS-2003-01

    Google Scholar 

  • Kooi B (2003b) Probabilistic dynamic epistemic logic. Journal of Logic, Language and Information 12(4):381–408

    Article  Google Scholar 

  • Kooi B (2007) Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics 17(2):231–253

    Article  Google Scholar 

  • Kooi B, van Benthem J (2004) Reduction axioms for epistemic actions. In: Schmidt R, Pratt-Hartmann I, Reynolds M, Wansing H (eds) AiML-2004: Advances in Modal Logic, Department of Computer Science, University of Manchester, Technical report series, UMCS-04-9-1, pp 197–211

    Google Scholar 

  • Kurucz A (2006) Combining modal logics. In: Blackburn P, van Benthem J, Wolter F (eds) Handbook of modal logic, studies in logic, vol 3, Elsevier, Amsterdam, pp 869–924

    Google Scholar 

  • Lindström S, Segerberg K (2007) Modal logic and philosophy. In: Blackburn P, van Benthem J, Wolter F (eds) Handbook of modal logic, studies in logic and practical reasoning, vol 3, Elsevier, Amsterdam, pp 1149–1214

    Google Scholar 

  • Lomuscio A, Ryan M (1997) On the relation between interpreted systems and kripke models. In: Proceedings of the AI97 Workshop on Theoretical and Practical Foundation of Intelligent Agents and Agent-Oriented Systems, vol LNCS p 1441

    Google Scholar 

  • Lomuscio AR, van der Meyden R, Ryan M (2000) Knowledge in multiagent systems: initial configurations and broadcasts. ACM Transactions on Computational Logic 1(2):247–284

    Article  Google Scholar 

  • Luce RD, Raiffa H (1957) Games and decisions. John Wiley and Sons, New York

    Google Scholar 

  • Lutz C (2006) Complexity and succinctness of public announcement logic. In: Proceedings AAMAS-06: Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, Hakodate, Japan

    Google Scholar 

  • McCarthy J, Hayes PJ (1969) Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence 4:463–502

    Google Scholar 

  • van der Meyden R (1994) Axioms for knowledge and time in distributed systems with perfect recall. In: Proceedings of the IEEE Symposium on Logic in Computer Science, pp 448–457

    Google Scholar 

  • van der Meyden R (1996) Finite state implementations of knowledge-based programs. In: Chandru V, Vinay V (eds) Proceedings of the Conference on the Foundations of Software Technology and Theoretical Computer Science, Springer-Verlag, Berlin, Lecture Notes in Computer Science, vol 1180, pp 31–50

    Google Scholar 

  • van der Meyden R (2007) Two applications of epistemic logic in computer security. In: Logic at the Crossroads, pp 207–222

    Google Scholar 

  • van der Meyden R, Wilke T (2007) Preservation of epistemic properties in security protocol implementations. In: Proceedings of Theoretical Aspects of Rationality and Knowledge

    Google Scholar 

  • van der Meyden R, Wong K (2003) Complete axiomatizations for reasoning about knowledge and branching time. Studia Logica 75(1):93–123

    Article  Google Scholar 

  • Meyer JJ, Veltman F (2007) Intelligent agents and common sense reasoning. In: Blackburn P, van Benthem J, Wolter F (eds) Handbook of modal logic, Elsevier, Amsterdam

    Google Scholar 

  • Miller J, Moss L (April 2005a) The undecidability of iterated modal relativization. Studia Logica 79:373–407

    Article  Google Scholar 

  • Myerson R (2004) Harsanyi’s games with incomplete information. Management Science 50(12):1818–1824

    Article  Google Scholar 

  • von Neumann J, Morgenstern O (1944) A theory of games and economic behaviour. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Pacuit E (2007a) Some comments on history based structures. Journal of Applied Logic 5(4):613–624

    Article  Google Scholar 

  • Pacuit E, Parikh R (2006) Social interaction, knowledge and social software. In: Interactive Computation: The New Paradigm, Springer, pp 441–462

    Google Scholar 

  • Pacuit E, Parikh R, Cogan E (2006) The logic of knowledge based obligation. Knowledge, Rationality and Action: A Subjournal of Synthese 149(2):311–341

    Google Scholar 

  • Parikh R (2003) Levels of knowledge, games, and group action. Research in Economics 57:267–281

    Article  Google Scholar 

  • Parikh R, Ramanujam R (1985) Distributed processes and the logic of knowledge. In: Logic of programs, Springer, Lecture Notes in Computer Science, vol 193, pp 256–268

    Google Scholar 

  • Plaza JA (2007) Logics of public communications. Synthese 158(2):165–179 (this paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, and Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24).

    Article  Google Scholar 

  • Ramanujam R, Suresh S (2005) Deciding knowledge properties of security protocols. In: Proceedings of Theoretical Aspects of Rationality and Knowledge, pp 219–235

    Google Scholar 

  • Ramsey F (1926) Truth and probability. In: Braithwaite R (ed) The foundations of mathematics and other logical essays, Routledge, London

    Google Scholar 

  • Reiter R (2001) Knowledge in action: Logical foundations for specifying and implementing dynamical systems. The MIT Press, Cambridge

    Google Scholar 

  • Renardel de Lavalette GR (2004) Changing modalities. Journal of Logic and Computation 14(2):253–278

    Google Scholar 

  • Renne B (2010) Public Communication in Justification Logic. Journal of Logic and Computation. doi:10.1093/logcom/exp/026

    Google Scholar 

  • Renne B (2007b) The relative expressivity of public and private communication in BMS logic. In: van Benthem J, Ju S, Veltman F (eds) A Meeting of the Minds: Proceedings of the Workshop on Logic, Rationality, and Interaction, Beijing, 2007, College Publications, London, Texts in Computer Science, vol 8, pp 213–229

    Google Scholar 

  • de Rijke M (1994) Meeting some neighbours. In: van Eijck J, Visser A (eds) Logic and information flow, The MIT Press, Cambridge, pp 170–195

    Google Scholar 

  • Ruan J (2004) Exploring the update universe. Master’s thesis, ILLC, Amsterdam

    Google Scholar 

  • Sack J (2008a) Extending probabilistic dynamic epistemic logic. In: Proceedings of the Workshop on Logic and Intelligent Interaction

    Google Scholar 

  • Sack J (2008b) Temporal languages for epistemic programs. Journal of Logic, Language and Information 17(2):183–216

    Article  Google Scholar 

  • Savage L (1954a) The foundations of statistics. John Wiley and Sons, New York, second revised edition published by Dover Publications, 1972

    Google Scholar 

  • Searle J (1985) The construction of social reality. The Free Press, New York

    Google Scholar 

  • Shoham Y, Leyton-Brown K (2009) Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press, Cambridge

    Google Scholar 

  • Velazquez-Quesada FR (2009) Inference and update. Synthese (Knowledge, Rationality & Action) 169(2):283–300

    Google Scholar 

  • Veltman F (1996) Defaults in update semantics. Journal of Philosophical Logic 25(3):221–261

    Article  Google Scholar 

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  1. Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, 9712, GL, Groningen, The Netherlands

    Barteld Kooi

  2. Center for Logic and Philosophy of Science, Tilburg University, 5000, LE, Tilburg, The Netherlands

    Eric Pacuit

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    Patrick Girard

  2. , Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, Groningen, 9712 GL, Netherlands

    Olivier Roy

  3. , Département de philosophie, Université du Québec à Montréal, C.P. 8888, Succursale Centre-Ville, Montreal, H3C 3P8, Canada

    Mathieu Marion

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Kooi, B., Pacuit, E. (2011). Logics of Rational Interaction. In: Girard, P., Roy, O., Marion, M. (eds) Dynamic Formal Epistemology. Synthese Library, vol 351. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0074-1_2

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