Abstract
In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is ‘fact p is true and you don’t know that’, after which you know that p, which entails the negation of the announcement formula. The announcement of such a formula in a given information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and ‘philosophical puzzles’ reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas.
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References
C.E. Alchourrón P. Gärdenfors D. Makinson (1985) ArticleTitle‘On the Logic of Theory Change: Partial Meet Functions for Contraction and Revision’ Journal of Symbolic Logic 50 510–530 Occurrence Handle10.2307/2274239
Baltag A., Moss L, Solecki S, (2003), ‘The Logic of Public Announcements, Common Knowledge and Private Suspicions’, Manuscript, originally presented at TARK 98.
J. Barwise (1981) ArticleTitle‘Scenes and other Situations’ Journal of Philosophy 78 IssueID7 369–397 Occurrence Handle10.2307/2026481
R. Fagin J Halpern Y Moses M Vardi (1995) Reasoning About Knowledge MIT Press Cambridge. Massachusetts
H. Freudenthal (1969) ArticleTitle‘Stating of the Sum-and-Product Problem’ Nieuw Archief voor Wiskunde (New Archive of Mathematics) 17 152
G. Gamow M Stern (1958) Puzzle-Math Macmillan London
P. Gärdenfors (1988) Knowledge in Flux Modeling the Dynamics of Epistemic States MIT Press
Gerbrandy, J.: (1999), Bisimulations on Planet Kripke, Ph.D. thesis, University of Amsterdam. ILLC Dissertation Series DS-1999-01.
J. Hintikka (1962) Knowledge and Belief, An Introduction to the Logic of the Two Notions Cornell University Press Ithaca & London
C.H. Kahn (1979) The Art and Thought of Heraclitus Cambridge University Press Cambridge
T. Kirkman (1847) ArticleTitle‘On a Problem in Combinations’ Cambridge and Dublin Mathematics Journal 2 191–204
J.L. Kvanvig (1998) ‘Paradoxes, Epistemic’ E Craig (Eds) Routledge Encyclopedia of Philosophy, Vol 7 Routledge London 211–214
K. Makarychev Y Makarychev (2001) ArticleTitle‘The Importance of Being Formal’ Mathematical Intelligencer 23 IssueID1 41–42 Occurrence Handle10.1007/BF03024516
McCarthy, J.: (1990), ‘Formalization of Two Puzzles Involving Knowledge’, In V. Lifschitz (ed.), Formalizing Common Sense: Papers by John McCarthy, Ablex Series in Artificial Intelligence, Ablex Publishing Corporation, Norwood, NJ. Available online at http://www-formal.stanford.edu/jmc/.
Y.O. Moses D Dolev J.Y. Halpern (1986) ArticleTitle‘Cheating Husbands and other Stories: A Case Study in Knowledge Action and Communication’ Distributed computing 1 IssueID3 167–176 Occurrence Handle10.1007/BF01661170
D.J. O’Connor (1948) ArticleTitle‘Pragmatic Paradoxes’ Mind 57 358–359
Plaza J. (1989), ‘Logics of Public Communications’, In Emrich M, Pfeifer M, M.~Hadzikadic and Ras Z, (eds.), Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, 201–216.
W.V.O. Quine (1953) ArticleTitle‘On a So-called Paradox’ Mind 62 65–67
M. Scriven (1951) ArticleTitle‘Paradoxical Announcements’ Mind 60 403–407
R.A. Sorensen (1988) Blindspots Clarendon Press Oxford
van Benthem, J. F. A. K.: (2002), ‘One is a Lonely Number’: On the Logic of Communication’, To be published in the Proceedings of the Logic Colloquium 2002.
van Ditmarsch, H. P.: (2000), Knowledge games, Ph.D. thesis, University of Groningen. ILLC Dissertation Series DS-2000-06.
H.P. Ditmarsch Particlevan (2002) ‘The Description of Game Actions in Cluedo’ L. Petrosian V Mazalov (Eds) Game Theory and Applications, Vol 8. Nova Science Publishers Commack NY USA 1–28
H.P. Ditmarsch Particlevan (2003) ArticleTitle‘The Russian Cards Problem’ Studia Logica 75 31–62 Occurrence Handle10.1023/A:1026168632319
van Ditmarsch H.P., van der Hoek W., Kooi B.P. (2005), ‘Dynamic Epistemic Logic’, Manuscript.
P. Weiss (1952) ArticleTitle‘The Prediction Paradox’ Mind 61 265–269
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An erratum to this article is available at http://dx.doi.org/10.1007/s11229-006-8493-6.
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Van Ditmarsch, H., Kooi, B. The Secret of My Success. Synthese 151, 201–232 (2006). https://doi.org/10.1007/s11229-005-3384-9
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DOI: https://doi.org/10.1007/s11229-005-3384-9