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The Ditmarsch Tale of Wonders

  • Conference paper
KI 2014: Advances in Artificial Intelligence (KI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8736))

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Abstract

We propose a dynamic logic of lying, wherein a ‘lie that φ’ (where φ is a formula in the logic) is an action in the sense of dynamic modal logic, that is interpreted as a state transformer relative to φ. The states that are being transformed are pointed Kripke models encoding the uncertainty of agents about their beliefs. Lies can be about factual propositions but also about modal formulas, such as the beliefs of other agents or the belief consequences of the lies of other agents.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Proc. of 7th TARK, pp. 43–56. Morgan Kaufmann (1998)

    Google Scholar 

  4. Baltag, A., Smets, S.: The logic of conditional doxastic actions. In: New Perspectives on Games and Interaction. Texts in Logic and Games 4, pp. 9–31. Amsterdam University Press (2008)

    Google Scholar 

  5. Bok, S.: Lying: Moral Choice in Public and Private Life. Random House, New York (1978)

    Google Scholar 

  6. Frankfurt, H.G.: On Bullshit. Princeton University Press (2005)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Gneezy, U.: Deception: The role of consequences. American Economic Review 95(1), 384–394 (2005)

    Article  Google Scholar 

  9. Grimm, J.L.K., Grimm, W.K.: Kinder- und Hausmärchen. Reimer (1814), vol. 1 (1812) and vol. 2 (1814)

    Google Scholar 

  10. Hales, J.: Refinement quantifiers for logics of belief and knowledge. Honours Thesis, University of Western Australia (2011)

    Google Scholar 

  11. Kartik, N., Ottaviani, M., Squintani, F.: Credulity, lies, and costly talk. Journal of Economic Theory 134, 93–116 (2006)

    Article  MathSciNet  Google Scholar 

  12. Kooi, B.: Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics 17(2), 231–254 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kooi, B., Renne, B.: Arrow update logic. Review of Symbolic Logic 4(4), 536–559 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Littlewood, J.E.: A Mathematician’s Miscellany. Methuen and Company (1953)

    Google Scholar 

  15. Liu, F., Wang, Y.: Reasoning about agent types and the hardest logic puzzle ever. Minds and Machines 23(1), 123–161 (2013)

    Article  Google Scholar 

  16. Mahon, J.E.: Two definitions of lying. Journal of Applied Philosophy 22(2), 21–230 (2006)

    Google Scholar 

  17. Plaza, J.A.: Logics of public communications. In: Proc. of the 4th ISMIS, pp. 201–216. Oak Ridge National Laboratory (1989)

    Google Scholar 

  18. Rott, H.: Der Wert der Wahrheit. In: Mayer, M. (ed.) Kulturen der Lüge, pp. 7–34. Böhlau-Verlag, Köln und Weimar (2003)

    Google Scholar 

  19. Sakama, C.: Formal definitions of lying. In: Proc. of 14th TRUST (2011)

    Google Scholar 

  20. Sakama, C., Caminada, M., Herzig, A.: A logical account of lying. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 286–299. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  21. Siegler, F.A.: Lying. American Philosophical Quarterly 3, 128–136 (1966)

    Google Scholar 

  22. Steiner, D.: A system for consistency preserving belief change. In: Proc. of the ESSLLI Workshop on Rationality and Knowledge, pp. 133–144 (2006)

    Google Scholar 

  23. Trivers, R.: The Folly of Fools – the logic of deceit and self-deception in human life. Basic Books (2011)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  26. van Ditmarsch, H.: Comments on ‘The logic of conditional doxastic actions’. In: New Perspectives on Games and Interaction. Texts in Logic and Games 4, pp. 33–44. Amsterdam University Press (2008)

    Google Scholar 

  27. van Ditmarsch, H.: Dynamics of lying. Synthese 191(5), 745–777 (2014)

    Article  MathSciNet  Google Scholar 

  28. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library, vol. 337. Springer (2007)

    Google Scholar 

  29. van Ditmarsch, H., van Eijck, J., Sietsma, F., Wang, Y.: On the logic of lying. In: van Eijck, J., Verbrugge, R. (eds.) Games, Actions and Social Software 2011. LNCS, vol. 7010, pp. 41–72. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  30. van Emde Boas, P., Groenendijk, J., Stokhof, M.: The Conway paradox: Its solution in an epistemic framework. In: Truth, Interpretation and Information: Selected Papers from the Third Amsterdam Colloquium, pp. 159–182. Foris Publications, Dordrecht (1984)

    Google Scholar 

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Author information

Authors and Affiliations

  1. LORIA — CNRS, Université de Lorraine, France

    Hans van Ditmarsch

Authors
  1. Hans van Ditmarsch
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Editor information

Editors and Affiliations

  1. Universität Bremen, Germany

    Carsten Lutz

  2. University of New South Wales, 2052, Sydney, NSW, Australia

    Michael Thielscher

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van Ditmarsch, H. (2014). The Ditmarsch Tale of Wonders. In: Lutz, C., Thielscher, M. (eds) KI 2014: Advances in Artificial Intelligence. KI 2014. Lecture Notes in Computer Science(), vol 8736. Springer, Cham. https://doi.org/10.1007/978-3-319-11206-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-11206-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11205-3

  • Online ISBN: 978-3-319-11206-0

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