Truth in Dialogue Logic and Game-Theoretical Semantics (GTS)
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28.09.2015
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Abstract
In this paper truth in two game-theoretical approaches is considered, namely: in dialogue logic of Paul Lorenzen and Kuno Lorenz and game-theoretical semantics proposed by Jaakko Hintikka and developed by Gabriel Sandu. In the course of the article the principal features of the semantic conceptions of game-theoretical semantics and dialogue logic are revealed and compared. Thus, two concepts of truth are considered, that is, truth in game-theoretical semantics and truth in dialogue logic. In both cases truth is defined as an existence of a winning strategy for the player defending the formula. The connection between those two consists in a possibility to transform the winning strategy for the player in one system into the winning strategy for the corresponding player in the other one following the exact and finite algorithm. The result of the comparison makes it possible to get a certain understanding of the relation between model-theoretical and proof-theoretical approaches.
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How to Cite
Pavlova A. M. Truth in Dialogue Logic and Game-Theoretical Semantics (GTS) // Logicheskie Issledovaniya / Logical Investigations. 2015. VOL. 21. № 2. C. 107-133.
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References
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Wells S., Reed Ch. Formal Dialectic Specification // Argumentation in MultiAgent Systems First International Workshop. 2004. P. 31–43.
Драгалина-Черная Е.Г. Границы логики: Онтологический поворот // Философия науки. 2009. № 14. С. 87–99.
Лисанюк Е.Н. Риторика и формальная диалектика // РАЦИО.ru. 2010. № 3. С. 26–42.
Alama J., Uckelman S.L. Lorenzen Dialogue Games as Logical Semantics // Internatinal colloquium. Inside arguments: Logic vs Argumentation theory (Portugal: Faculty of Letters of the University of Coimbra, March 24-26, 2011). 2011. P. 1–14.
Barth E.M. From Axiom to Dialogue: a philosophical study of logics and argumentation. Berlin: Walter de Gruyter, 1982. 337 p.
van Benthem J. Logical Construction Games // Acta Philosophica Fennica. 2006. Vol. 78. P. 123–138.
Eklund M. On How Logic Became First-Order // Nordic Journal of Philosophical Logic. 1996. Vol. 1. № 2. P. 147–167.
Eklund M., Kolak D. Is Hintikka’s Logic First-Order? // Synthese. 2002. Vol. 131. Issue 3. P. 371–388.
Feferman S. What Kind of Logic is ‘Independence-Friendly’ Logic? // The Philosophy of Jaakko Hintikka / Ed. by Auxier. R.E., Hahn L.E. Chicago: Open Court, 2006. P. 453—469.
Godel K. Uber die Vollstandigkeit des Logikkalk_uls (1929) // Godel Collected Works / Ed. by S. Feferman. Vol. I, Publications 1929–1936. Oxford University Press, 1986. P. 61–101.
Hamblin Ch. Fallacies. London: Methuen, 1970. 336 p.
Hintikka J. The Principles of Mathematics Revisited. Cambridge University Press, Cambridge, 1996. 304 p.
Hintikka J. Post-Tarskian Truth // Synthese. 2001. Vol. 126. P. 17–36.
Hintikka J., Sandu G. What is Logic? // Handbook of the Philosophy of Logic / Ed. by D. Jacquette. Amsterdam: Elsevier, 2007. P. 13–40.
Hodges W. Compositional Semantics for a Langauge of Imperfect Information // Logic Journal of the IGPL. 1997. Vol. 5. P. 539—563.
Krabbe E.C.W. Dialogue logic // Handbook of the History of Logic. 2006. Vol. 7. P. 665–704.
Lorenz K. Arithmetik und Logik als Spiele. PhD thesis, Universit_at Kiel, 1961. Selections reprinted in [19].
Lorenzen P. Constructive philosophy / Transl. by Pavlowic. Amherst: University of Massachusetts Press, 1987. 291 p.
Lorenzen P., Lorenz K. Dialogische Logik. Darmstadt: Wissenschaftlische Buchgesellschaft, 1978. 238 p.
Pietarinen Aht. Varieties of IFing // Proceedings of the ESSLLI’01 Workshop on Logic and Games / Ed. by G. Sandu and M. Pauly. Department of Philosophy, University of Helsinki, 2001. P. 25–32.
Rahman Sh. Remarks on Dialogical Meaning: A Case Study, 2011. URL: http://ls.informatik.uni-tuebingen.de/prodi/slides/Rahman.pdf (дата обращения: 21.04.2015).
Rahman Sh., Ruckert H. Preface // Synthese. 2001. Vol. 127. P. 1–6.
Rahman Sh., Tulenheimo T. From Games to Dialogues and Back: Towards a General Frame for Validity // Games: Unifying logic, Language and Philosophy / Ed. by Ondrej Majer, Ahti-Veikko Pietarinen, Tero Tulenheimo. Springer, 2009. P. 153–208.
Reed Ch, Walton D. Argumentation Schemes in Dialogue // Dissensus and the Search for Common Ground (Proceedings of OSSA 2007) / Ed. by H.V. Hansen, et al. Volume CD-ROM. 2007. P. 1–11.
de Rouihan P., Bozon S. The Truth of IF: Has Hintikka Really Exorcised Tarski’s Curse? // The Philosophy of Jaakko Hintikka. The Library of Liveing Philosophers. Vol. XXX. 2006. P. 683–705.
Stegmuller W. Remarks on the completeness of logical systems relative to the validity-concepts of P. Lorenzen and K. Lorenz // Notre Dame J. Formal Logic. 1964. Vol. 5. № 2. P. 81–112.
Uckelman S.L., Johnston S. A Simple Semantics for Aristotelian Apodictic Syllogistics // Advances in Modal Logic. 2010. Vol. 8. P. 428–443.
Weingartner P. Basic Questions on Truth. Kluwer Academic Publishers, 2000. 244 p.
Wells S., Reed Ch. Formal Dialectic Specification // Argumentation in MultiAgent Systems First International Workshop. 2004. P. 31–43.