Abstract
In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical proposi-tional logic and for classical first-order logic, an exact connection between ‘in-tuitionistic dialogues with hypotheses’ and semantic games is established. Various questions of a philosophical nature are also shown to arise as a result of the comparison, among them the relation between the model-theoretic and proof-theoretic approaches to the philosophy of logic and mathematics.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blackburn, P., de Rijke, M., and Venema, Y. (2002). Modal Logic. Cambridge University Press, Cambridge.
Blass, A. (1992). A game semantics for linear logic. Annals of Pure and Applied Logic, 56: 183–220.
Carlson, L. (1983). Dialogue Games. An Approach to Discourse Analysis. Reidel, Dordrecht.
Dascal, M., Hintikka, J., and Lorenz, K. (1995). Jeux dans le langage/Games in Language/Spiel in der Sprache. In Dascal, M., Gerhardus, D., Lorenz, K., and Meggle, G., editors, Sprach-philosophie/Philosophy of Language/La Philosophie du langage, pages 1371–1390. De Gruyter, Berlin.
Felscher, W. (1985). Dialogues, strategies and intuitionistic provability. Annals of Pure and Applied Logic, 28:217–254.
Haas, G. (1980). Hypothesendialoge, konstruktiver Sequenzenkalköl und die Rechtfertigung von Dialograhmenregeln. In Gethmann, C. F., editor, Theorie des wissenschaftlichen Argu-mentierens, pages 136–161. Suhrkamp, Frankfurt.
Henkin, L. (1950). Completeness in the theory of types. Journal of Symbolic Logic, 15(2): 81–91.
Henkin, L. (1961). Some remarks on infinitely long formulas. In Infinitistic Methods, pages 167–183. Pergamon, Oxford.
Hintikka, J. (1968). Language-games for quantifiers. Americal Philosophical Quarterly Monograph Series 2: Studies in Logical Theory. Basil Blackwell, Oxford.
Hintikka, J. (1973). Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. Clarendon, Oxford.
Hintikka, J. (1987). Game-theoretical semantics as a synthesis of verificationist and truth-conditional meaning theories. In LePore, E., editor, New Directions in Semantics. Academic, London.
Hintikka, J. (1993). The original Sinn of Wittgenstein's philosophy of mathematics. In Puhl, K., editor, Wittgenstein's Philosophy of Mathematics, pages 24–51. Hölder—Pichler—Tempsky, Vienna.
Hintikka, J. (1996). The Principles of Mathematics Revisited. Cambridge University Press, Cambridge.
Hintikka, J. (2002). Hyperclassical logic (a.k.a. IF logic) and its implications for logical theory. Bulletin of Symbolic Logic, 8(3):404–423.
Hintikka, J. and Rantala, V. (1976). A new approach to infinitary languages. Annals of Mathematical Logic, 10:95–115.
Hintikka, J. and Sandu, G. (1997). Game-theoretical semantics. In van Benthem, J. and ter Meulen, A., editors, Handbook of Logic and Language, pages 361–410. Elsevier, Amsterdam.
Hintikka, M. B. and Hintikka, J. (1986). Investigating Wittgenstein. Basil Blackwell, Oxford.
Hodges, W. (1997). Model theory. In Rota, G.-C., editor, Encyclopedia of Mathematics and Its Applications, volume 42. Cambridge University Press, Cambridge. First published 1993.
Hodges, W. (2006). Logic and games. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy (Summer 2006 Edition). http://plato.stanford.edu/archives/sum2006/ entries/logic-games/.
Hyttinen, T. (1990). Model theory for infinite quantifier logics. Fundamenta Mathematicæ, 134:125–142.
Kamlah, W. and Lorenzen, P. (1973). Logische Propädeutik. Bibilographisches Institut, Mannheim.
Karttunen, M. (1984). Model theory for infinitely deep languages. Annales Academiæ Scien-tiarum Fennicæ, 50.
Kontchakov, R., Kurucz, A., and Zakharyaschev, M. (2005). Undecidability of first-order intu-itionistic and modal logics with two variables. Bulletin of Symbolic Logic, 11(3):428–438.
Krynicki, M. and Mostowski, M. (1995). Henkin quantifiers. In Krynicki, M., Mostowski, M., and Sczerba, L. W., editors, Quantifiers: Logics, Models and Computation, volume 1, pages 193–262. Kluwer, Dordrecht.
Lorenz, K. (1961). Arithmetik und Logik als Spiele. Ph.D. thesis, Christian-Albrechts-Universität Zu Kiel.
Lorenz, K. (1970). Elemente der Sprachkritik. Suhrkamp, Frankfurt.
Lorenz, K. (2001). Basic objectives of dialogue logic in historical perspective. Synthese, 127:255–263.
Lorenzen, P. and Lorenz, K. (1978). Dialogische Logik. Wissenschaftliche Buchgesellschaft, Darmstadt.
Lorenzen, P. and Schwemmer, O. (1975). Konstruktive Logik, Ethik und Wissenschaftstheorie. Bibilographisches Institut, Mannheim.
Makkai, M. (1977). Admissible sets and infinitary logic. In Barwise, J., editor, Handbook of Mathematical Logic, pages 233–281. North-Holland, Amsterdam.
Osborne, M. J. and Rubinstein, A. (1994). A Course in Game Theory. MIT, Cambridge, MA.
Rahman, S. (1994). Über Dialoge, Protologische Kategorien und andere Seltenheiten. Peter Lang, Frankfurt.
Rahman, S. and Keiff, L. (2005). On how to be a dialogician. In Vanderveken, D., editor, Logic, Thought and Action, volume 2: Logic, Epistemology and Unity of Science, pages 359–408. Springer, Dordrecht.
Ranta, A. (1988). Propositions as games as types. Synthese, 76:377–395.
Saarinen, E. (1978). Dialogue semantics versus game-theoretical semantics. In Proceedings of the Biennial Meeting of the Philosophy of Science Association (PSA), volume 2: Symposia and Invited Papers, pages 41–59. The University of Chicago Press, Chicago, IL.
Sandu, G. and Pietarinen, A.-V. (2001). Partiality and games: Propositional logic. Logic Journal of the IGPL, 9(1):107–127.
Sandu, G. and Pietarinen, A.-V. (2003). Informationally independent connectives. In Mints, G. and Muskens, R., editors, Games, Logic, and Constructive Sets, pages 23–41. CSLI, Stanford.
Schwalbe, U. and Walker, P. (2001). Zermelo and the early history of game theory. Games and Economic Behaviour, 34:123–137.
Skolem, Th. (1920). Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Be-weisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen. Skrifter utgit av Videnskabsselskapet i Kristiania, I. Matematisk-naturvidenskabelig klasse no. 4.
Stegmüller, W. (1964). Remarks on the completeness of logical systems relative to the validity-concepts of P. Lorenzen and K. Lorenz. Notre Dame Journal of Formal Logic, 5:81–112.
Sundholm, G. (2002). Proof theory and meaning. In Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, volume 9, pages 165–198. Kluwer, Dordrecht, second edition.
Tarski, A. (1983). The concept of truth in the languages of the deductive sciences. In Corcoran, J., editor, A. Tarski: Logic, Semantics, Metamathematics. Papers from 1923 to 1938, pages 152–278. Hackett, Indianapolis, IN. Polish; original in Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno—Fizycznych 34, Warsawm, 1933.
Tarski, A. and Vaught, R. L. (1956). Arithmetical extensions of relational systems. Compositio Mathematica, 13:81–102.
van Benthem, J. (2001a). Games in dynamic epistemic logic. Bulletin of Economic Research, 53(4):219–248. Proceedings LOFT-4, Torino, Bonanno, G. and van der Hoek, W., editors.
van Benthem, J. (2001b). Logic and Games. Lecture Notes (Draft Version), ILLC, Amsterdam.
van Benthem, J. (2002). Extensive games as process models. Journal of Logic, Language and Information, 11:289–313.
Vaught, R. L. (1973). Descriptive set theory in lε1ε. In Mathias, A. and Rogers, H., editors, Cambridge Summer School in Mathematical Logic, volume 337 of Lecture Notes in Mathematics, pages 574–598. Springer, Berlin.
von Neumann, J. and Morgenstern, O. (2004). Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ, sixtieth-anniversary edition. (First appeared in 1944.)
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
Rahman, S., Tulenheimo, T. (2009). From Games to Dialogues and Back. 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_8
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9374-6_8
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)