Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T03:09:55.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Logic in a Social Setting

Published online by Cambridge University Press:  03 January 2012

Johan van Benthem
Get access Rights & Permissions [Opens in a new window]

Abstract

Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.

Type
Research Article
Information
Episteme , Volume 8 , Issue 3 , October 2011 , pp. 227 - 247
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aumann, R. 1995. “Backward Induction and Common Knowledge of Rationality.” Games and Economic Behavior 8(1): 6–19.Google Scholar
Baltag, A. and Smets, S.. 2008. “A Qualitative Theory of Dynamic Interactive Belief Revision.” In Bonanno, G., Hoek, W. van der, and Wooldridge, M. (eds.), Texts in Logic and Games Vol. 3, pp. 9–58Amsterdam: Amsterdam University Press.Google Scholar
Baltag, A. and Smets, S.. 2009. “Group Belief Dynamics under Iterated Revision: Fixed Points and Cycles of Joint Upgrades.” Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 41–50. New York: ACM.CrossRefGoogle Scholar
Baltag, A., Smets, S., and Zvesper, J.. 2009. “Keep ‘Hoping’ for Rationality: A Solution to the Backward Induction Paradox.” Synthese 169: 301–33.Google Scholar
Bicchieri, C. 1988. “Common Knowledge and Backward Induction: A Solution to the Paradox.” Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 381–93. Los Altos, CA: Morgan Kaufmann Publishers.Google Scholar
Blackburn, P., de Rijke, M., and Venema, Y.. 2000. Modal Logic. Cambridge: Cambridge University Press.Google Scholar
Brandenburger, A. 2007. “Forward Induction.” Manuscript, Stern School of Business, New York University.Google Scholar
Dégrémont, C., Kurzen, L., and Szymanik, J.. 2011. “Cognitive Plausibility of Epistemic Models: Exploring Tractability Borders in Epistemic Tasks.” Manuscript, ILLC, University of Amsterdam.Google Scholar
Dégrémont, C. and Roy, O.. 2009. “Agreement Theorems in Dynamic Epistemic Logic.” In Heifetz, A. (ed.), Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 91–8 New York: ACM.Google Scholar
Gheerbrant, A. 2010. Fixed-Point Logics on Trees. Dissertation, ILLC, University of Amsterdam.Google Scholar
Gierasimczuk, N. 2010. Knowing One's Limits: Logical Analysis of Inductive Inference. Dissertation, ILLC, University of Amsterdam.Google Scholar
Girard, P. 2008. Modal Logic for Belief and Preference Change. Dissertation, Department of Philosophy, Stanford University, and ILLC, University of Amsterdam.Google Scholar
Halpern, J. and Vardi, M.. 1989. “The Complexity of Reasoning about Knowledge and Time, I: Lower Bounds.” Journal of Computer and System Sciences 38: 195–237.Google Scholar
Hoshi, T. 2009. Epistemic Dynamics and Protocol Information. Dissertation, Department of Philosophy, Stanford University.Google Scholar
Joyce, J. 2004. “Bayesianism.” In Mele, A. and Rawling, P. (eds.), The Oxford Handbook of Rationality, pp. 132–55 Oxford: Oxford University Press.Google Scholar
Kelly, K. 1996. The Logic of Reliable Inquiry. Oxford: Oxford University Press.Google Scholar
Liu, F. 2011. Reasoning about Preference Dynamics. Dordrecht: Springer.Google Scholar
Parikh, R., Tasdemir, C., and Witzel, A. 2011. “The Power of Knowledge in Games.” Working paper, CUNY Graduate Center and New York University.Google Scholar
Perea, A. 2011. “Belief in the Opponents' Future Rationality.” Working paper, Epicenter, Department of Quantitative Economics, University of Maastricht.Google Scholar
Stalnaker, R. 1999. “Extensive and Strategic Form: Games and Models for Games.” Research in Economics 53: 293–319.Google Scholar
van Benthem, J. 1996. Exploring Logical Dynamics. Stanford: CSLI Publications.Google Scholar
van Benthem, J. 2004. “Update and Revision in Games.“ Lecture notes, ILLC, University of Amsterdam and Stanford University.Google Scholar
van Benthem, J. 2007a. “Dynamic Logic of Belief Revision.” Journal of AppliedNon-Classical Logics 17: 129–55.Google Scholar
van Benthem, J. 2007b. “Rational Dynamics.” International Game Theory Review 9(1): 13–45. Erratum reprint, 9(2): 377–409.CrossRefGoogle Scholar
van Benthem, J. 2007c. “Rationalizations and Promises in Games.” Philosophical Trends, Supplement 2006, pp. 1–6Beijing: Chinese Academy of Social Sciences.Google Scholar
van Benthem, J. 2011. Logical Dynamics of Information and Interaction. Cambridge: Cambridge University Press.Google Scholar
van Benthem, J., Gerbrandy, J., Hoshi, T., and Pacuit, E.. 2009. “Merging Frameworks for Interaction.” Journal of Philosophical Logic 38: 491–526.Google Scholar
van Benthem, J. and Gheerbrant, A.. 2010. “Game Solution, Epistemic Dynamics and Fixed-Point Logics.” Fundamenta Informaticae 100: 1–23.Google Scholar
van Benthem, J., van Otterloo, S., and Roy, O.. 2006. “Preference Logic, Conditionals, and Solution Concepts in Games.” In Lagerlund, H., Lindström, S., and Sliwinski, R. (eds.), Modality Matters, pp. 61–76Uppsala: University of Uppsala.Google Scholar
van Benthem, J., Pacuit, E., and Roy, O.. 2011. “Games and Interaction: The Logical Perspective.” Games 2(1): 52–86.CrossRefGoogle Scholar
van der Hoek, W. and Pauly, M.. 2006. “Modal Logic for Games and Information.” In Blackburn, P., van Benthem, J., and Wolter, F. (eds.), Handbook of Modal Logic, pp. 1077–148. Amsterdam: Elsevier.Google Scholar
von Wright, G. H. 1963. The Logic of Preference. Edinburgh: Edinburgh University Press.Google Scholar