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Merging Information

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Games, Norms and Reasons

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Abstract

On innumerous occasions in our everyday life we are forced to make decisions on the basis of incomplete information that we acquire regarding the current state of affairs. While playing poker, we are forced to decide whether to bet without being sure about the opponents’ hands; we have imperfect information about the situation of the game. Scheduling cricket matches in the nor’western season is just like a game of chance; there is no guarantee that a match would be played on the scheduled day because of the possibility of the sudden storms, and one has to depend on weather forecasts which are invariably incomplete in terms of their information content.

* Acknowledges NWO grant # 600.065.120.08N201

** Acknowledges a scholarship by Consejo Nacional de Ciencia y Tecnología (CONACyT) from México. Scholarship holder # 167693

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References

  1. C.E. Alchourròn, P. Gardenfors, and D. Makinson. On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50(2):510–530, 1985.

    Article  Google Scholar 

  2. H. Andréka, M.D. Ryan, and P.-Y. Schobbens. Operators and laws for combining preference relations. Journal of Logic and Computation, 12(1):13–53, 2002.

    Article  Google Scholar 

  3. C. Areces and B. ten Cate. Hybrid logics. In P. Blackburn, J. van Benthem, and F. Wolter, editors, Handbook of Modal Logic, volume 3 of Studies in Logic and Practical reasoning. Elsevier, Amsterdam, The Netherlands, 2005.

    Google Scholar 

  4. K.J. Arrow. A difficulty in the concept of social welfare. Journal of Political Economy, 58:328–346, 1950.

    Article  Google Scholar 

  5. C. Balkenius and P. Gärdenfors. Nonmonotonic inferences in neural networks. In J.A. Allen, R. Fikes, and E. Sandewall, editors, Principles of knowledge representation and reasoning, pages 32–39. Morgan Kaufmann, San Mateo, CA, 1991.

    Google Scholar 

  6. A. Baltag, L.S. Moss, and S. Solecki. The logic of public announcements, common knowledge and private suspicious. Technical Report SEN-R9922, CWI, Amsterdam, 1999.

    Google Scholar 

  7. A. Baltag and S. Smets. Conditional doxastic models: A qualitative approach to dynamic belief revision. Electronic Notes in Theoretical Computer Science, 165:5–21, 2006.

    Article  Google Scholar 

  8. A. Baltag and S. Smets. Dynamic belief revision over multi-agent plausibility models. In W. van der Hoek and M. Wooldridge, editors, Proceedings of LOFT 2006, pages 11–24. University of Liverpool, Liverpool, 2006. Available at http://www.vub.ac.be/CLWF/SS/loft.pdf

    Google Scholar 

  9. A. Baltag and S. Smets. A qualitative theory of dynamic interactive belief revision. In G. Bonanno, W. van der Hoek, and M. Wooldridge, editors, Logic and the Foundation of Game and Decision Theory (LOFT7), volume 3 of Texts in Logic and Games, pages 13–60. Amsterdam University Press, Amsterdam, The Netherlands, 2008.

    Google Scholar 

  10. P. Blackburn, M. de Rijke, and Y. Venema. Modal Logic. Cambridge University Press, Cambridge, 2001.

    Google Scholar 

  11. R. Blutner and P.D. Doherty. Nonmonotonic logic and neural networks. Available at http://citeseer.ist.psu.edu/160749.html

  12. A. d’Avila Garcez, K. Broda, and D. Gabbay. Symbolic knowledge extraction from trained neural networks: A sound approach. Artificial Intelligence, 125(1–2):155–207, January 2001.

    Article  Google Scholar 

  13. J. de Kleer. An assumption-based truth maintenance system. Artificial Intelligence, 28(2):127–162, 1986.

    Article  Google Scholar 

  14. J. de Kleer. A perspective on assumption-based truth maintenance. Artificial Intelligence, 59(1–2):63–67, 1993.

    Article  Google Scholar 

  15. M. de Rijke. Extending Modal Logic. PhD thesis, Institute for Logic, Language and Computation (Universiteit van Amsterdam), 1993. ILLC Dissertation Series DS-1993–04.

    Google Scholar 

  16. M. de Rijke. Meeting some neighbours. In J. van Eijk and A. Viser, editors, Logic and Information Flow, pages 170–196. The MIT Press, Cambridge, MA, 1994.

    Google Scholar 

  17. E. Lorini and R. Demolombe. From binary trust to graded trust in information sources: a logical perspective. In Trust in Agent Societies, Lecture Notes in Computer Science, volume 5396, pages 205–225. Springer, Berlin, 2008.

    Google Scholar 

  18. J. Doyle. A truth maintenance system. Artificial Intelligence, 12(3):231–272, 1979.

    Article  Google Scholar 

  19. D. Eckert and G. Pigozzi. Belief merging, judgment aggregation and some links with social choice theory. In J.P. Delgrande, J. Lang, H. Rott, and J.-M. Tallon, editors, Belief Change in Rational Agents, volume 05321 of Dagstuhl Seminar Proceedings. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany, 2005.

    Google Scholar 

  20. A. Fuhrmann. Reflective modalities and theory change. Synthese, 81(1):115–134, October, 1989.

    Article  Google Scholar 

  21. D.M. Gabbay, G. Pigozzi, and O. Rodrigues. Common foundations for belief revision, belief merging and voting. In G. Bonanno, J.P. Delgrande, J. Lang, and H. Rott, editors, Formal Models of Belief Change in Rational Agents, volume 07351 of Dagstuhl Seminar Proceedings. Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany, 2007.

    Google Scholar 

  22. H. Gaifman. Operational pointer semantics: solution to self-referential puzzles i. In TARK ’88: Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning About Knowledge, pages 43–59. Morgan Kaufmann Publishers Inc., San Francisco, CA, 1988.

    Google Scholar 

  23. H. Gaifman. Pointers to truth. Journal of Philosophy, 5(89):223–261, 1992.

    Article  Google Scholar 

  24. J. Gerbrandy. Bisimulations on Planet Kripke. PhD thesis, Institute for Logic, Language and Computation (Universiteit van Amsterdam), 1999. ILLC Dissertation Series DS-1999–01.

    Google Scholar 

  25. J. Gerbrandy. Dynamic epistemic logic. In L.S. Moss, J. Ginzburg, and M. de Rijke, editors, Logic, Language and Computation, volume 2, pages 67–84. Center for the Study of Language and Information, Stanford, CA, 1999.

    Google Scholar 

  26. S. Ghosh, B. Löwe, and E. Scorelle. Belief flow in assertion networks. In U. Priss, S. Polovina, and R. Hill, editors, Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007), Sheffield, UK, volume 4604 of LNAI, pages 401–414. Springer, Heidelberg, July 2007.

    Google Scholar 

  27. S. Ghosh and F.R. Veläzquez-Quesada. Expressing belief flow in assertion networks. In P. Bosch, D. Gabelaia, and J. Lang, editors, TbiLLC, volume 5422 of Lecture Notes in Computer Science, pages 124–138. Springer, Berlin, Germany, 2007.

    Google Scholar 

  28. P. Girard. Modal Logic for Belief and Preference Change. PhD thesis, Department of Philosophy (Stanford University), Stanford, CA, February 2008. ILLC Dissertation Series DS-2008–04.

    Google Scholar 

  29. A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17(2):157–170, May 1988.

    Article  Google Scholar 

  30. A. Gupta and N.D. Belnap. The Revision Theory of Truth. The MIT Press, Cambridge, MA, 1993.

    Google Scholar 

  31. S. Ove Hansson. A survey of non-prioritized belief revision. Erkenntnis, 50(2–3):413–427, 1999.

    Article  Google Scholar 

  32. W.L. Harper. Rational conceptual change. In Proceedings of the Meeting of the Philosophy of Science Association (PSA 1976), volume 2, pages 462–494. Philosophy of Science Association, The University of Chicago Press, Chicago, IL, 1977.

    Google Scholar 

  33. H.G. Herzberger. Naive semantics and the liar paradox. The Journal of Philosophy, 79:479–497, 1982.

    Article  Google Scholar 

  34. S. Konieczny. Sur la logique du changement: Révision et fusion de bases de connaissance. PhD thesis, Laboratoire d’Informatique Fondamentale de Lille, Université de Lille 1, Lille, France, November 1999.

    Google Scholar 

  35. S. Konieczny and R. Pino-Pérez. On the logic of merging. In Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR’98), pages 488–498. Morgan Kaufmann, Trento, June 2–5, 1998.

    Google Scholar 

  36. S. Konieczny and R. Pino-Pérez. Merging information under constraints: A logical framework. Journal of Logic and Computation, 12(5):773–808, 2002.

    Article  Google Scholar 

  37. S. Konieczny and R. Pino-Pérez. Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory. European Journal of Operational Research, 160(3):785–802, 2005.

    Article  Google Scholar 

  38. H. Leitgeb. Interpreted dynamical systems and qualitative laws: From neural networks to evolutionary systems. Synthese, 146(1–2):189–202, August 2005.

    Article  Google Scholar 

  39. H. Leitgeb and K. Segerberg. Dynamic doxastic logic: Why, how, and where to? Synthese, 155(2):167–190, 2007.

    Article  Google Scholar 

  40. I. Levi. Subjunctives, dispositions, and chances. Synthese, 34:423–455, 1977.

    Article  Google Scholar 

  41. I. Levi. The Enterprise of Knowledge. MIT Press, Cambridge, MA, 1980.

    Google Scholar 

  42. D.K. Lewis. Counterfactuals. Blackwell, Cambridge, MA, 1973.

    Google Scholar 

  43. E. Lorini and R. Demolombe, Trust and norms in the context of computer security: a logical formalization. In van der Meyden, Ron and van der Torre, Leendert editors, Deontic Logic in Computer Science, LNCS 5076, pages 50–64, Springer, Berlin, 2008.

    Chapter  Google Scholar 

  44. T. Meyer A.K. Ghose and S. Chopra. Non-prioritized ranked belief change. Journal of Philosophical Logic, 32(4):117–143, 2003.

    Google Scholar 

  45. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, Santa Mateo, CA, September 1988.

    Google Scholar 

  46. J. Plaza. Logics of public communications. In M.L. Emrich, M.S. Pfeifer, M. Hadzikadic, Z. Ras, editors, Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, pages 201–216. Charlotte, NC, 1989.

    Google Scholar 

  47. K. Segerberg. Belief revision from the point of view of doxastic logic. Logic Journal of IGPL, 3(4):535–553, 1995.

    Article  Google Scholar 

  48. K. Segerberg. Two traditions in the logic of belief: Bringing them together. In H.J. Ohlbach and U. Reyle, editors, Logic, Language and Reasoning. Essays in Honour of Dov Gabbay, pages 135–147. Kluwer Academic Publishers, Dordrecht, 1999.

    Chapter  Google Scholar 

  49. B. ten Cate. Model theory for extended modal languages. PhD thesis, Institute for Logic, Language and Computation (Universiteit van Amsterdam), 2005. ILLC Dissertation Series DS-2005–01.

    Google Scholar 

  50. J. van Benthem. Semantic parallels in natural language and computation. In Logic Colloquium ‘87, pages 331–375. Elsevier Science Publishers, Amsterdam, 1989.

    Google Scholar 

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

    Article  Google Scholar 

  52. J. van Benthem. Priority product update as social choice. Available at http://dare.uva.nl/document/93918, 2007.

  53. J. van Benthem, P. Girard, and O. Roy. Everything else being equal: A modal logic approach for ceteris paribus preferences. Journal of Philosophical Logic, 38:83–125, 2009.

    Article  Google Scholar 

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

    Article  Google Scholar 

  55. J. van Benthem, S. van Otterloo, and O. Roy. Preference logic, conditionals and solution concepts in games. In Festschrift for Krister Segerberg. University of Uppsala, Uppsala, 2005.

    Google Scholar 

  56. H. van Ditmarsch, W. van der Hoek, and B. Kooi. Dynamic Epistemic Logic, volume 337 of Synthese Library Series. Springer, Berlin, Germany, 2007.

    Google Scholar 

  57. J. Williamson. Bayesian Nets and Causality: Philosophical and Computational Foundations. Oxford University Press, Oxford, 2005.

    Google Scholar 

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Correspondence to Sujata Ghosh* .

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Ghosh*, S., Velázquez-Quesada**, F.R. (2011). Merging Information. In: van Benthem, J., Gupta, A., Pacuit, E. (eds) Games, Norms and Reasons. Synthese Library, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0714-6_5

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