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Part of the book series: Logic, Epistemology, And The Unity Of Science ((LEUS,volume 1))

Abstract

The purpose of this paper is to introduce the reader to game-theoretic semantics (GTS), and to chart some of its current directions, with a focus on epistemological issues. GTS was originally developed by Jaakko Hintikka in the 1960s and became one of the main approaches in logical and linguistic semantics. The theory has been researched in numerous publications. I will put games in a wider historical and systematic perspective within the overall development of logic, and explore some of the recent advances.

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References

  • Bacharach, M. O. L., Gérard-Varet, L.-A., Mongin, P., and Shin, H. S., (eds.): 1997, Epistemic Logic and the Theory of Games and Decisions, Dordrecht, Kluwer.

    Google Scholar 

  • van Benthem, Johan: 2003, ‘Hintikka Self-applied’, to appear in R. E. Auxier and L. E. Hahn (eds.), Library of Living Philosophers: Jaakko Hintikka. Available electronically at http://turing.wins.uva.nl/~johan/H-H.ps.

  • Boolos, George: 1981, ‘For All A there is a B’, Linguistic Inquiry 12, 465–467.

    Google Scholar 

  • Borel, Emil: 1921, ‘La théorie du jeu et les equations intégrales á noyau symétrique’, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences 173, 1304–1308. (Translation by L. J. Savage: 1953. ‘The Theory of Play and Integral Equations with Skew Symmetric Kernels’, Econometrica 21, 97–100.)

    Google Scholar 

  • Copeland, B. Jack: 2002, ‘The Genesis of Possible Worlds Semantics’, Journal of Philosophical Logic 31, 99–137.

    Article  Google Scholar 

  • Doherty, Patrik (ed.): 1996, Partiality, Modality, and Nonmonotonicity, Stanford, CSLI Publications.

    Google Scholar 

  • Felscher, Walter: 2002, ‘Dialogues as a Foundation for Intuitionistic Logic’, in Gabbay, D. and Guenthner, F. (eds.), Handbook of Philosophical Logic 5, (2nd edn), Dordrecht, Kluwer, pp. 115–146.

    Google Scholar 

  • Geach, Peter: 1967, ‘Intentional Identity’, Journal of Philosophy 64, 627–632.

    Article  Google Scholar 

  • Gentzen, Gerhard: 1969, ‘The Consistency of Elementary Number Theory’, in M. E. Szabo (ed.), The Collected Works of Gerhard Gentzen, Amsterdam, North-Holland, pp. 132–213.

    Google Scholar 

  • Harsanyi, John C.: 1967, ‘Games with Incomplete Information Played by ‘Bayesian’ Players. Part I: The Basic Model’, Management Science 14, 159–182.

    Article  Google Scholar 

  • Henkin, Leon: 1961, ‘Some Remarks on Infinitely Long Formulas’, in (no editor given) Infinistic Methods. Proceedings of the Symposium on Foundations of Mathematics, Warsaw, Panstwowe (2–9 September 1959), Naukowe: Wydawnictwo, New York, Pergamon Press, pp. 167–183.

    Google Scholar 

  • Hilpinen, Risto: 1982, ‘On C. S. Peirce's Theory of the Proposition: Peirce as a Precursor of Game-theoretical Semantics’, The Monist 62, 182–189.

    Google Scholar 

  • Hintikka, Jaakko: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Ithaca, Cornell University Press.

    Google Scholar 

  • Hintikka, Jaakko: 1973, Logic, Language-Games and Information, Oxford, Oxford University Press.

    Google Scholar 

  • Hintikka, Jaakko: 1975, ‘Impossible Possible Worlds Vindicated’, Journal of Philosophical Logic 4, 475–484.

    Article  Google Scholar 

  • Hintikka, Jaakko: 1996, The Principles of Mathematics Revisited, New York, Cambridge University Press.

    Google Scholar 

  • Hintikka, Jaakko and Gabriel Sandu: 1989, ‘Informational Independence as a Semantical Phenomenon’, in J. E. Fenstad, I. T. Frolov and R. Hilpinen (eds.), Logic, Methodology and Philosophy of Science, Vol. 8, Amsterdam, North-Holland, pp. 571–589.

    Google Scholar 

  • Hintikka, Jaakko and Gabriel Sandu: 1997, ‘Game-theoretical Semantics’, in J. van Benthem, and A. ter Meulen (eds.), Handbook of Logic and Language, Amsterdam, Elsevier, pp. 361–410.

    Chapter  Google Scholar 

  • Hintikka, Jaakko, Ilpo Halonen and Arto Mutanen: 2002, ‘Interrogative Logic’, in D. M. Gabbay, R. H. Johnson, H. J. Ohlbach and J. Woods (eds.), Handbook of the Logic of Argument and Inference. The Turn Towards the Practical, Dordrecht, Kluwer, pp. 295–337.

    Chapter  Google Scholar 

  • Hodges, Wilfrid: 1997, ‘Games in Logic’, in P. Dekker, M. Stokhof and Y. Venema (eds.), Proceedings of the 11th Amsterdam Colloquium, Amsterdam, University of Amsterdam, pp. 13–18.

    Google Scholar 

  • Isbell, John: 1957, ‘Finitary Games’, in D. Dresher, A. W. Tucker and P. Wolfe (eds.), Contributions to the Theory of Games, Vol. 3, Princeton, Princeton University Press, pp. 79–96.

    Google Scholar 

  • Janssen, Theo M. V.: 2002. ‘On the Interpretation of IF Logic’, Journal of Logic, Language and Information 11, 367–387.

    Article  Google Scholar 

  • Jervell, Hermann R.: 1985, ‘Gentzen Games’, Zeitschrift für Mathematische Logic und Grundlagen der Mathematik 31, 431–439.

    Article  Google Scholar 

  • Kalmár, László: 1928–1929, ‘Zur Theorie der abstrakten Spiele’, Acta Scientiarum Mathematicarum (Szeged), 4, 65–85. (Translation: ‘On the Theory of Abstract Games’, in M. A. Dimand, and R. W. Dimand (eds.), The Foundations of Game Theory, Vol. 1, Cheltenham, Edward Elgar, 1997, pp. 247–262.)

    Google Scholar 

  • Kelly, Kevin: 1996, The Logic of Reliable Inquiry, New York, Oxford University Press.

    Google Scholar 

  • Kelly, Kevin and Clark Glymour: 1990, ‘Theory Discovery form Data with Mixed Quantifiers’, Journal of Philosophical Logic 19, 1–33.

    Article  Google Scholar 

  • König, Dénes: 1927, ‘Über eine Schlußweise aus dem Endlichen ins Unendliche’ (‘On a Consequence of Passing from the Finite to the Infinite’), Acta Scientiarum Mathematicarum (Szeged) 3, 121–130.

    Google Scholar 

  • Kratzer, Angelica: 1998, ‘Scope or Pseudoscope? Are there Wide-scope Indefinites?’, in S. Rothstein (ed.), Events in Grammar, Dordrecht, Kluwer, pp. 163–196.

    Google Scholar 

  • Kreps, David M. and Robert B. Wilson: 1982, ‘Sequential Equilibria’, Econometrica 50, 863–894.

    Article  Google Scholar 

  • Kretzmann, Norman and Eleonore Stump: 1988, The Cambridge Translations of Medieval Philosophical Texts, Vol. 1, Melbourne, Cambridge University Press.

    Google Scholar 

  • Kuhn, Harold W.: 1953, ‘Extensive Games and the Problem of Information’, in H. W. Kuhn, and A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. 2, Princeton, Princeton University Press, pp. 193–216.

    Google Scholar 

  • Langholm, Tore: 1996, ‘How Different is Partial Logic?’, in P. Doherty (ed.), Partiality, Modality, and Nonmonotonicity, Stanford, CSLI, pp. 3–43.

    Google Scholar 

  • Leibniz, Gottfried W.: 1981, New Essays on Human Understanding (Translated and edited by P. Remnant, P. and J. Bennett), Cambridge, Cambridge University Press.

    Google Scholar 

  • Lorenz, Kuno: 1961, Arithmetic und Logic als Spiele, dissertation, Universität Kiel. (Partially reprinted in Lorenzen and Lorenz 1978).

    Google Scholar 

  • Lorenz, Kuno: 2001, ‘Basic Objectives of Dialogue Logic in Historical Perspective’, Synthese 127, 255–263.

    Article  Google Scholar 

  • Lorenzen, Paul: 1955, ‘Einführung in die operative Logik und Mathematik’, Die Grundlehren der mathematischen wissenschaften 78, Berlin, Springer

    Google Scholar 

  • Lorenzen, Paul and Lorenz, Kuno: 1978, Dialogische Logic, Darmstadt, Wissenschaftliche Buchgesellschaft.

    Google Scholar 

  • Luce, R. Duncan and Howard Raiffa: 1957, Games and Decisions, New York, John Wiley.

    Google Scholar 

  • Mann, William C.: 1988, ‘Dialogue Games: Conventions of Human Interaction’, Argumentation 2, 511–532.

    Article  Google Scholar 

  • Maynard Smith, John: 1982, Evolution and the Theory of Games, Cambridge, Cambridge University Press.

    Google Scholar 

  • Morgenstern, Oskar: 1976, Selected Economic Writings of Oskar Morgenstern, Andrew Schotter (ed.), New York, New York University Press.

    Google Scholar 

  • von Neumann, John: 1928, ‘Zur Theorie der Gesellschaftsspiele’, Mathematische Annalen 100, 295–320. (Translation by S. Bargmann: ‘On the Theory of Games of Strategy’, in A. W. Tucker, and R. D. Luce (eds.), Contributions to the Theory of Games, Vol. 4, Princeton, Princeton University Press, 1959, pp. 13–42.)

    Article  Google Scholar 

  • von Neumann, John: 1953, ‘Communication on the Borel Notes’, Econometrica 21, 124–125.

    Article  Google Scholar 

  • von Neumann, John and Oskar Morgenstern: 1944, Theory of Games and Economic Behavior, New York, John Wiley.

    Google Scholar 

  • Peirce, Charles S.: 1931–1935, in C. Hartshorne and P. Weiss (eds.), Collected Papers, Vols. 1–6, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Peirce, Charles S.: 1967, Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin, Annotated Catalogue of the Papers of Charles S. Peirce (Amherst, University of Massachusettes Press, 1967), and in ‘The Peirce Papers: A Supplementary Catalogue’, Transactions of the C. S. Peirce Society 7 (1971), 37–57.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2000, ‘Logic and Coherence in the Light of Competitive Games’, Logique et Analyse 171–172, 371–391.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2001a, ‘Intentional Identity Revisited’, Nordic Journal of Philosophical Logic 6, 144–188.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2001b, ‘Most Even Budged Yet: Some Cases for Game-theoretic Semantics in Natural Language’, Theoretical Linguistics 27, 20–54.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2001c, ‘Propositional Logic of Imperfect Information: Foundations and Applications’, Notre Dame Journal of Formal Logic 42, 193–210.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2002a, ‘Knowledge Constructions for Artificial Intelligence’, in M.-S. Hacid, Z. W. Ras, D. A. Zighed and Y. Kodratoff (eds.), Foundations of Intelligent Systems, Lecture Notes in Artificial Intelligence 2366, Springer, pp. 303–311.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2002b, ‘Games and Logics of Knowledge for Multi-agent Systems’, in C. A. Coello Coello, A. de Albornoz, L. E. Sucar and O. C. Battistutti (eds.), Advances in Artificial Intelligence, Lecture Notes in Artificial Intelligence 2313, Springer, pp. 214–223.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2002c, ‘Negotiation Games and Conflict Resolution in Logical Semantics’, in Paolo Boquet (ed.), Meaning Negotiation: Papers from the AAAI Workshop (MeaN-02), Technical Report WS-02-09, AAAI Press, pp. 25–31.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2003a, ‘Peirce's Game-theoretic Ideas in Logic’, Semiotica 144, 33–47.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2003b, ‘A Note on the Structural Notion of Information in Extensive Games’, Quality & Quantity 37, 91–98.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2003c, ‘Peirce's Theory of Communication and its Contemporary Relevance’, in Kristóf NyÍri (ed.), Mobile Learning: Essays on Philosophy, Psychology and Education, Vienna, Passagen Verlag, pp. 81–98.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2003d, ‘What do Epistemic Logic and Cognitive Science have to Do with Each Other?’, Cognitive Systems Research 4, 169–190.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2003e, ‘Games and Formal Tools Versus Games as Explanations in Logic and Science’, Foundations of Science 8, 317–364.

    Article  Google Scholar 

  • Pietarinen, Ahti-Veikko: 2003f, ‘What is a Negative Polarity Item?’, Linguistic Analysis 31, 165–200.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2004a, ‘Diagrammatic Logic and Game-playing’, to appear in Grant Malcolm (ed.), Multidisciplinary Approaches to Visual Representations and Interpretations, Elsevier.

    Google Scholar 

  • Pietarinen, Ahti-Veikko: 2004b, ‘IF Logic and Incomplete Information’, to appear in J. van Benthem et al. (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today, Kluwer.

    Google Scholar 

  • Pietarinen, Ahti-Veikko and Gabriel Sandu: 1999, ‘Games in Philosophical Logic’, Nordic Journal of Philosophical Logic 4, 143–173.

    Google Scholar 

  • Pietarinen, Ahti-Veikko and Gabriel Sandu: 2004, ‘IF Logic, Game-theoretical Semantics and the Philosophy of Science’, this volume.

    Google Scholar 

  • Rahman, Shahid and Helge Rückert: 2001, ‘Dialogical Connexive Logic’, Synthese 127, 105–139.

    Article  Google Scholar 

  • Rantala, Veikko: 1982, ‘Impossible Worlds and Logical Omniscience’, Acta Philosophica Fennica 35, 106–115.

    Google Scholar 

  • Sandu, Gabriel: 1993, ‘On the Logic of Informational Independence and its Applications’, Journal of Philosophical Logic 22, 29–60.

    Article  Google Scholar 

  • Sandu, Gabriel and Ahti-Veikko Pietarinen: 2001, ‘Partiality and Games: Propositional Logic’, Logic Journal of the IGPL 9, 107–127.

    Article  Google Scholar 

  • Sandu, Gabriel and Ahti-Veikko Pietarinen: 2003, ‘Informationally Independent Connectives’, in G. Mints and R. Muskens (eds.), Games, Logic, and Constructive Sets, Stanford, CSLI Publications, pp. 23–41.

    Google Scholar 

  • Scott, Dana: 1993, ‘A Game-theoretical Interpretation of Logical Formulae’ (manuscript original 1968), Jahrbuch 1991 der Kurt-Goedel-Gesellschaft, Wien, Kurt-Goedel-Gesellschaft, pp. 47– 48.

    Google Scholar 

  • Skolem, Thoralf: 1920, ‘Logico-combinatorial Investigations in the Satisfiability or Provability of Mathematical Propositions: A Simplified Proof of a Theorem by L. Löwenheim and Generalizations of the Theorem’, in J. van Heijenoort (ed.), 1967, From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA, Harvard University Press, pp. 254–263. (Original: ‘Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit und Be-weisbarkeit mathematischen Sätze nebst einem Theoreme über dichte Mengen’, Skrifter utgit av Videnskabsselskapet i Kristiania, Vol. 1, Matematisk-naturvidenskabelig klasse 4, 1–36. Reprinted in Skolem, T.: 1970, in J. E. Fenstad (ed.), Selected Works in Logic, Oslo, Universitetsforlaget, pp. 103–136.)

    Google Scholar 

  • Stalnaker, Robert: 1999, ‘Extensive and Strategic Forms: Games and Models for Games’, Research in Economics 53, 293–319.

    Article  Google Scholar 

  • Steels, Luc: 1998, ‘Synthesizing the Origins of Language and Meaning using Coevolution, Self-organization and Level Formation’, in J. R. Hurford, M. Studdert-Kennedy and C. Knight (eds.), Evolution of Language: Social and Cognitive Bases, Cambridge, Cambridge University Press, pp. 384–404.

    Google Scholar 

  • Strotz, Robert H.: 1956, ‘Myopia and Inconsistency in Dynamic Utility Maximization’, Review of Economic Studies 23, 165–180.

    Google Scholar 

  • Suppe, Frederick: 1989, The Semantic Conception of Theories and Scientific Realism, University of Illinois Press.

    Google Scholar 

  • Tennant, Neil: 1998, ‘Games Some People Would Have All of Us Play', Critical Study/Book Review of Hintikka 1996’, Philosophia Mathematica 6, 90–115.

    Google Scholar 

  • Turner, Ken: 1999, The Semantics/Pragmatics Interface from Different Points of View, Current Research in the Semantics/Pragmatics Interface Vol. 1, Oxford, Elsevier.

    Google Scholar 

  • Ulam, Stanislaw M.: 1958, ‘John von Neumann, 1903–1957’, Bulletin of the American Mathematical Society 64, 1–49.

    Article  Google Scholar 

  • Väänänen, Jouko: 2001, ‘Second-order Logic and the Foundations of Mathematics’, Bulletin of Symbolic Logic 7, 504–520.

    Article  Google Scholar 

  • Wittgenstein, Ludwig: 1978, Philosophical Grammar, Columbia, University of California Press.

    Google Scholar 

  • Wittgenstein, Ludwig: 2000, Wittgenstein's Nachlass, The Bergen Electronic Edition, The Wittgenstein Trustees, The University of Bergen, Oxford University Press. (The transcription used is the diplomatic transcription.)

    Google Scholar 

  • Zermelo, Ernst: 1913, ‘Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels’, in E. W. Hobson, and A. E. H. Love (eds.), Proceedings of the Fifth International Congress of Mathematicians, Vol. 2, Cambridge, Cambridge University Press, pp. 501–504. (Translation by Schwalbe, Ulrich and Paul Walker: ‘On an Application of Set Theory to the Theory of the Game of Chess’, in Schwalbe, Ulrich and Paul Walker: 2001, ‘Zermelo and the Early History of Game Theory’, Games and Economic Behaviour 34, 123–137.)

    Google Scholar 

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Pietarinen, AV. (2009). Semantic Games In Logic and Epistemology. In: Rahman, S., Symons, J., Gabbay, D.M., Bendegem, J.P.v. (eds) Logic, Epistemology, and the Unity of Science. Logic, Epistemology, And The Unity Of Science, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2808-3_6

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