Logics of Rational Interaction

Chapter
Part of the Synthese Library book series (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.

References

  1. Ågotnes T, Alechina N (2007) The dynamics of syntactic knowledge. Journal of Logic and Computation 17(1):83–116CrossRefGoogle Scholar
  2. Alchourrón C, Gärdenfors P, Makinson D (1985) On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50:510–530CrossRefGoogle Scholar
  3. 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):385–403Google Scholar
  4. Artemov S, Nogina E (2005) Introducing justification into epistemic logic. Journal of Logic and Computation 15(6):1059–1073CrossRefGoogle Scholar
  5. Aucher G (2003) A combined system for update logic and belief revision. Master’s thesis, ILLC, University of Amsterdam, AmsterdamGoogle Scholar
  6. Aucher G (2007) Interpreting an action from what we perceive and what we expect. Journal of Applied Non-Classical Logics 17(1):9–38CrossRefGoogle Scholar
  7. 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 CrossRefGoogle Scholar
  8. Aumann R (1976) Agreeing to disagree. Annals of Statistics 4:1236–1239CrossRefGoogle Scholar
  9. Aumann R (1999) Interactive epistemology I: Knowledge. International Journal of Game Theory 28:263–300CrossRefGoogle Scholar
  10. 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 42–51Google Scholar
  11. Baltag A (2002) A logic for suspicious players: epistemic actions and belief-updates in games. Bulletin of Economic Research 54(1):1–45CrossRefGoogle Scholar
  12. Baltag A, Moss LS (2004) Logics for epistemic programs. Synthese 139(2):165–224CrossRefGoogle Scholar
  13. 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 9–58Google Scholar
  14. 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 43–56Google Scholar
  15. 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 56Google Scholar
  16. 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, AmsterdamGoogle Scholar
  17. van Benthem J (2001) Games in dynamic-epistemic logic. Bulletin of Economic Research 53(4):219–248CrossRefGoogle Scholar
  18. van Benthem J (2003) Conditional probability meets update logic. Journal of Logic, Language and Information 12(4):409–421CrossRefGoogle Scholar
  19. van Benthem J (2004) What one may come to know. Analysis 64(2):95–105CrossRefGoogle Scholar
  20. van Benthem J (2005) Rational animals: What is ‘KRA’?, http://staff.science.uva.nl/johan/publications.html, invited lecture Malaga ESSLLI Summer School 2006
  21. 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
  22. van Benthem J (2007) Dynamic logic for belief revision. Journal of Applied Non-Classical Logics 17(2):129–155CrossRefGoogle Scholar
  23. van Benthem J (2008a) Logical dynamics of information and interaction. Book manuscriptGoogle Scholar
  24. van Benthem J (2008b) Merging observation and access in dynamic logic. ManuscriptGoogle Scholar
  25. van Benthem J (2010) Logical dynamics of information and interaction. ILLC Manuscript, to appear with Cambridge University PressGoogle Scholar
  26. van Benthem J, Dégremont C (2009) Building bridges between dynamic and temporal doxastic logics. In: Proceedings of LOFT 8Google Scholar
  27. 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 146–165Google Scholar
  28. van Benthem J, Liu F (2007) Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2):157–182CrossRefGoogle Scholar
  29. 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 87–106Google Scholar
  30. van Benthem J, van Eijck J, Kooi B (2006) Logics of communication and change. Information and Computation 204(11):1620–1662CrossRefGoogle Scholar
  31. van Benthem J, Gerbrandy J, Hoshi T, Pacuit E (2009a) Merging frameworks of interaction. Journal of Philosophical Logic 38:491–526CrossRefGoogle Scholar
  32. van Benthem J, Gerbrandy J, Kooi B (2009b) Dynamic update with probabilities. Studia Logica 93(1):67–96CrossRefGoogle Scholar
  33. Blackburn P, de Rijke M, Venema Y (2002) Modal logic. Cambridge University Press, CambridgeGoogle Scholar
  34. Bleeker A, van Eijck J (2000) The epistemics of encryption. Tech. Rep. INS-R0019, CWI, Amsterdam, available from http://db.cwi.nl/rapporten/
  35. Bonanno G (2004) Memory and perfect recall in extensive games. Games and Economic Behaviour 47:237–256CrossRefGoogle Scholar
  36. Bonanno G (2007) Axiomatic characterization of AGM belief revision in a temporal logic. Artificial Intelligence 171:144–160CrossRefGoogle Scholar
  37. Bonanno G, Battigalli P (1999) Recent results on belief, knowledge and the epistemic foundations of game theory. Research in Economics 53(2):149–225CrossRefGoogle Scholar
  38. Brandenburger A (2007) The power of paradox: some recent developments in interactive epistemology. International Journal of Game Theory 35:465–492CrossRefGoogle Scholar
  39. Bratman M (1987) Intention, plans and practical reason. Harvard University Press, LondonGoogle Scholar
  40. Bratman M (2007) Structures of agency. Oxford University Press, OxfordGoogle Scholar
  41. Cantwell J (2006) A formal model of multi-agent belief-interaction. Journal of Logic, Language and Information 15(4):303–329CrossRefGoogle Scholar
  42. Cartwright N (2007) Hunting causes and using them: Approaches in philosophy and economics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  43. 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 129–143Google Scholar
  44. 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 87–117Google Scholar
  45. van Ditmarsch H, van der Hoek W, Kooi B (2007) Dynamic epistemic logic. Synthese library, Springer, New YorkGoogle Scholar
  46. van Ditmarsch HP (2003) The Russian cards problem. Studia Logica 75:31–62CrossRefGoogle Scholar
  47. van Ditmarsch HP (2005) Prolegomena to dynamic logic for belief revision. Synthese (Knowledge, Rationality & Action) 147:229–275Google Scholar
  48. van Ditmarsch HP, Kooi B (2006) The secret of my success. Synthese 151(2):201–232CrossRefGoogle Scholar
  49. 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 141–148CrossRefGoogle Scholar
  50. van Ditmarsch HP, van der Hoek W, van der Meyden R, Ruan J (2006) Model checking russian cards. Electronic Notes in Theoretical Computer Science 149:790–795Google Scholar
  51. Duc HN (1997) Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 7(5):633–648CrossRefGoogle Scholar
  52. Duc HN (2001) Resource-bounded reasoning about knowledge. PhD thesis, Universität LeipzigGoogle Scholar
  53. van Eijck J (2004a) Guarded actions. Tech. Rep. SEN-E0425, CWI, Amsterdam, available from http://db.cwi.nl/rapporten/
  54. 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/
  55. van Eijck J (2005) DEMO: a system for dynamic epistemic modeling. http://homepages.cwi.nl/jve/demo
  56. 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 44–59Google Scholar
  57. Fagin R, Halpern J, Moses Y, Vardi M (1995) Reasoning about knowledge. The MIT Press, BostonGoogle Scholar
  58. 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 YorkGoogle Scholar
  59. 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 107–123Google Scholar
  60. 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 53–72Google Scholar
  61. Friedman N, Halpern J (1997) Modeling belief in dynamic systems. Part I: Foundations. Artificial Intelligence 95(2):257–316CrossRefGoogle Scholar
  62. Friedman N, Halpern J (1999) Modeling belief in dynamic systems. Part II: Revision and update. Journal of AI Research 10:117–167Google Scholar
  63. Gerbrandy J (1999a) Bisimulations on planet kripke. PhD thesis, Institute for Logic, Language and Computation (DS-1999-01)Google Scholar
  64. Gerbrandy J, Groeneveld W (1997) Reasoning about information change. Journal of Logic, Language and Information 6(2):147–169CrossRefGoogle Scholar
  65. Gerbrandy JD (2007) The surprise examination in dynamic epistemic logic. Synthese 155(1):21–33CrossRefGoogle Scholar
  66. Grimm J, Grimm W (1857) Kinder- und Hausmärchen. GöttingenGoogle Scholar
  67. Halpern J (1999) Set-theoretic completeness for epistemic and conditional logic. Annals of Mathematics and Artificial Intelligence 26:1–27CrossRefGoogle Scholar
  68. Halpern J, Pucella R (2003) Modeling adversaries in a logic for security protocol analysis. In: Formal Aspects of SecurityGoogle Scholar
  69. Halpern J, Vardi M (1989) The complexity of reasoning about knowledge and time. Journal of Computer and System Sciences 38:195–237CrossRefGoogle Scholar
  70. Halpern J, van der Meyden R, Vardi M (2004) Complete axiomatizations for reasoning about knowledge and time. SIAM Journal of Computing 33(2):674–703CrossRefGoogle Scholar
  71. Halpern J (2003) Reasoning about Uncertainty. The MIT Press, Cambridge, MAGoogle Scholar
  72. Harsanyi J (1967) Games with incomplete informations played by ‘bayesian’ players. Management Science 14:159–182, 320–334, 486–502CrossRefGoogle Scholar
  73. 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 409–418CrossRefGoogle Scholar
  74. Herzig A, Lang J, Polacsek T (2000b) A modal logic for epistemic tests. In: Horn W (ed) Proceedings of ECAI 2000, pp 553–557Google Scholar
  75. 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 655–720Google Scholar
  76. 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 1077–1148Google Scholar
  77. van der Hoek W, Wooldridge M (2003) Towards a logic of rational agency. Logic Journal of the IGPL 11(2):135–160CrossRefGoogle Scholar
  78. Hommersom A, Meyer JJC, de Vink E (2004) Update semantics of security protocols. Synthese (Knowledge, Rationality & Action) 142:229–267Google Scholar
  79. Horty J (2001a) Agency and deontic logic. Oxford University Press, OxfordCrossRefGoogle Scholar
  80. Hoshi T, Yap A (2009) Dynamic epistemic logic with branching temporal structures. Synthese (Knowledge, Rationality & Action)Google Scholar
  81. Hyman J, Steward H (eds) (2004) Agency and action. Cambridge University Press, CambridgeGoogle Scholar
  82. Jago M (2006) Logics for resource-bounded agents. PhD thesis, University of NottinghamGoogle Scholar
  83. Kooi B (2003a) Knowledge, chance, and change. PhD thesis, University of Groningen, iLLC Dissertation Series DS-2003-01Google Scholar
  84. Kooi B (2003b) Probabilistic dynamic epistemic logic. Journal of Logic, Language and Information 12(4):381–408CrossRefGoogle Scholar
  85. Kooi B (2007) Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics 17(2):231–253CrossRefGoogle Scholar
  86. 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 197–211Google Scholar
  87. 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 869–924Google Scholar
  88. 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 1149–1214Google Scholar
  89. 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 1441Google Scholar
  90. Lomuscio AR, van der Meyden R, Ryan M (2000) Knowledge in multiagent systems: initial configurations and broadcasts. ACM Transactions on Computational Logic 1(2):247–284CrossRefGoogle Scholar
  91. Luce RD, Raiffa H (1957) Games and decisions. John Wiley and Sons, New YorkGoogle Scholar
  92. 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, JapanGoogle Scholar
  93. McCarthy J, Hayes PJ (1969) Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence 4:463–502Google Scholar
  94. 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 448–457Google Scholar
  95. 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 31–50Google Scholar
  96. van der Meyden R (2007) Two applications of epistemic logic in computer security. In: Logic at the Crossroads, pp 207–222Google Scholar
  97. van der Meyden R, Wilke T (2007) Preservation of epistemic properties in security protocol implementations. In: Proceedings of Theoretical Aspects of Rationality and KnowledgeGoogle Scholar
  98. van der Meyden R, Wong K (2003) Complete axiomatizations for reasoning about knowledge and branching time. Studia Logica 75(1):93–123CrossRefGoogle Scholar
  99. 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, AmsterdamGoogle Scholar
  100. Miller J, Moss L (April 2005a) The undecidability of iterated modal relativization. Studia Logica 79:373–407CrossRefGoogle Scholar
  101. Myerson R (2004) Harsanyi’s games with incomplete information. Management Science 50(12):1818–1824CrossRefGoogle Scholar
  102. von Neumann J, Morgenstern O (1944) A theory of games and economic behaviour. Princeton University Press, Princeton, NJGoogle Scholar
  103. Pacuit E (2007a) Some comments on history based structures. Journal of Applied Logic 5(4):613–624CrossRefGoogle Scholar
  104. Pacuit E, Parikh R (2006) Social interaction, knowledge and social software. In: Interactive Computation: The New Paradigm, Springer, pp 441–462Google Scholar
  105. Pacuit E, Parikh R, Cogan E (2006) The logic of knowledge based obligation. Knowledge, Rationality and Action: A Subjournal of Synthese 149(2):311–341Google Scholar
  106. Parikh R (2003) Levels of knowledge, games, and group action. Research in Economics 57:267–281CrossRefGoogle Scholar
  107. 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 256–268Google Scholar
  108. 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).CrossRefGoogle Scholar
  109. Ramanujam R, Suresh S (2005) Deciding knowledge properties of security protocols. In: Proceedings of Theoretical Aspects of Rationality and Knowledge, pp 219–235Google Scholar
  110. Ramsey F (1926) Truth and probability. In: Braithwaite R (ed) The foundations of mathematics and other logical essays, Routledge, LondonGoogle Scholar
  111. Reiter R (2001) Knowledge in action: Logical foundations for specifying and implementing dynamical systems. The MIT Press, CambridgeGoogle Scholar
  112. Renardel de Lavalette GR (2004) Changing modalities. Journal of Logic and Computation 14(2):253–278Google Scholar
  113. Renne B (2010) Public Communication in Justification Logic. Journal of Logic and Computation. doi:10.1093/logcom/exp/026Google Scholar
  114. 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 213–229Google Scholar
  115. de Rijke M (1994) Meeting some neighbours. In: van Eijck J, Visser A (eds) Logic and information flow, The MIT Press, Cambridge, pp 170–195Google Scholar
  116. Ruan J (2004) Exploring the update universe. Master’s thesis, ILLC, AmsterdamGoogle Scholar
  117. Sack J (2008a) Extending probabilistic dynamic epistemic logic. In: Proceedings of the Workshop on Logic and Intelligent InteractionGoogle Scholar
  118. Sack J (2008b) Temporal languages for epistemic programs. Journal of Logic, Language and Information 17(2):183–216CrossRefGoogle Scholar
  119. Savage L (1954a) The foundations of statistics. John Wiley and Sons, New York, second revised edition published by Dover Publications, 1972Google Scholar
  120. Searle J (1985) The construction of social reality. The Free Press, New YorkGoogle Scholar
  121. Shoham Y, Leyton-Brown K (2009) Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press, CambridgeGoogle Scholar
  122. Velazquez-Quesada FR (2009) Inference and update. Synthese (Knowledge, Rationality & Action) 169(2):283–300Google Scholar
  123. Veltman F (1996) Defaults in update semantics. Journal of Philosophical Logic 25(3):221–261CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Faculty of PhilosophyUniversity of GroningenGroningenThe Netherlands
  2. 2.Center for Logic and Philosophy of Science, Tilburg UniversityTilburgThe Netherlands

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