Abstract
Hintikka and Sandu's Independence-friendly logic (Hintikka, 1996; Hintikka and Sandu, 1997) has traditionally been associated with extensive games of imperfect information. In this paper we set up a strategic framework for the evaluation of IF logic à la Hintikka and Sandu. We show that the traditional semantic interpretation of IF logic can be characterized in terms of Nash equilibria. We note that moving to the strategic framework we get rid of IF semantic games that violate the principle of perfect recall. We explore the strategic framework by replacing the notion of Nash equilibrium by other solution concepts, that are inspired by weakly dominant strategies and iterated removal thereof, charting the expressive power of IF logic under the resulting semantics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cameron, P. J. and Hodges, W. (2001). Some combinatorics of imperfect information. Journal of Symbolic Logic, 66(2):673–684.
de Bruin, B. (2004). Explaining Games, On the Logic of Game Theoretic Explanations. Ph.D. thesis, ILLC, Universiteit van Amsterdam.
Dechesne, F. (2005). Game, Set, Maths: Formal Investigations into Logic with Imperfect Information. Ph.D. thesis, SOBU, Tilburg university and Technische Universiteit Eindhoven.
Henkin, L. (1959). Some remarks on infinitely long formulas. Infinitistic Methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 167–183.
Hintikka, J. (1996). Principles of Mathematics Revisited. Cambridge University Press, Cambridge.
Hintikka, J. and Sandu, G. (1997). Game-theoretical semantics. In van Benthem, J. F. A. K. and ter Meulen, A., editors, Handbook of Logic and Language, pages 361–481. North Holland, Amsterdam.
Janssen, T. M. V. (2002). Independent choices and the interpretation of IF logic. Journal of Logic, Language and Information, 11:367–387.
Osborne, M. J. and Rubinstein, A. (1994). A Course in Game Theory. MIT, Cambridge, MA. Pietarinen, A. and Tulenheimo, T. (2004). An introduction to IF logic. Lecture notes for the 16th European Summer School in Logic, Language and Information.
Sandu, G. and Pietarinen, A. (2003). Informationally independent connectives. In Mints, G. and Muskens, R., editors, Logic, Language and Computation, volume 9, pages 23–41. CSLI, Stanford.
Sevenster, M. (2006). Branches of Imperfect Information: Logic, Games, and Computation. Ph.D. thesis, ILLC, University of Amsterdam.
van Benthem, J. F. A. K. (2000). Logic and games, lecture notes. Draft version.
van Benthem, J. F. A. K. (2004). Probabilistic features in logic games. In Kolak, D. and Symons, D., editors, Quantifiers, Questions and Quantum Physics, pages 189–194. Springer, Dordrecht.
Walkoe, W. (1970). Finite partially-ordered quantification. Journal of Symbolic Logic, 35: 535–555.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V.
About this chapter
Cite this chapter
Sevenster, M. (2009). A Strategic Perspective on if Games. In: Majer, O., Pietarinen, AV., Tulenheimo, T. (eds) Games: Unifying Logic, Language, and Philosophy. Logic, Epistemology, and the Unity of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9374-6_5
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9374-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9373-9
Online ISBN: 978-1-4020-9374-6
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)