Abstract
We explain Giles's characterization of Lukasiewicz logic via a dialogue game combined with bets on results of experiments that may show dispersion. The game is generalized to other fuzzy logics and linked to recent results in proof theory. We argue that these results allow one to place t-norm based fuzzy logics in a common framework with supervaluation as a theory of vagueness.
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
Avron, A. (1991). Hypersequents, logical consequence and intermediate logics for concurrency. Annals of Mathematics and AI, 4(3–4):225–248.
Burns, L. C. (1991). Vagueness: An Investigation Into Natural Language and the Sorites Paradox. Kluwer, Dordrecht.
Ciabattoni, A. and Fermüller, C. G. (2003). From intuitionistic logic to gödel-dummett logic via parallel dialogue games. In 33rd Intl. Symp. on Multiple-Valued Logic, pages 188–195. IEEE Computer Society Press, Tokyo.
Ciabattoni, A., Fermüller, C. G., and Metcalfe, G. (2005). Uniform rules and dialogue games for fuzzy logics. In Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2004, Springer LNAI 3452, 496–510, Dordrecht.
Cignoli, R., D'Ottaviano, I. M. L., and Mundici, D. (1999). Algebraic Foundations of Many-Valued Reasoning, volume 7 of Trends in Logic. Kluwer, Dordrecht.
Dubois, D. and Prade, H. (1980). Fuzzy Sets and Systems: Theory and Applications. Academic, New York.
Esteva, F., Godo, L., Hájek, P., and Montagna, F. (2003). Hoops and fuzzy logic. Journal of Logic and Computation, 13(4):532–555.
Felscher, W. (1985). Dialogues, strategies, and intuitionistic provability. Annals of Pure and Applied Logic, 28:217–254.
Fermüller, C. G. (2003a). Parallel dialogue games and hypersequents for intermediate logics. In TABLEAUX 2003, volume 2796 of LNAI, pages 48–64. Springer, Dordrecht.
Fermüller, C. G. (2003b). Theories of vagueness versus fuzzy logic: can logicians learn from philosophers? Neural Network World Journal, 13(5):455–466.
Fine, K. (1975). Vagueness, truth and logic. Synthèse, 30:265–300.
Giles, R. (1974). A non-classical logic for physics. Studia Logica, 4(33):399–417.
Giles, R. (1977). A non-classical logic for physics. In Wojcicki, R. and Malinkowski, G., editors, Selected Papers on Łukasiewicz Sentential Calculi, pages 13–51. Polish Academy of Sciences, Wroclaw — Warszawa — Kraków — Gdańsk.
Hájek, P. (1998). Metamathematics of Fuzzy Logic. Kluwer, Dordrecht.
Hájek, P. (2002). Why fuzzy logic? In Jackquette, D., editor, A Companion to Philosophical Logic, pages 595–606. Blackwell, Oxford.
Keefe, R. (2000). Theories of Vagueness. Cambridge University Press, Cambridge.
Keefe, R. and Smith, P., editors (1987). Vagueness: A Reader. MIT Press, Cambridge, MA.
Krabbe, E. C. W. (1988). Dialogue sequents and quick proofs of completeness. In Hoepelman, J. P., editor, Representation and Reasoning, pages 135–140. Max Niemeyer Verlag, Tübingen.
Kremer, P. and Kremer, M. (2003). Some supervaluation-based consequence relations. Journal of Philosophical Logic, 32(3):225–244.
Lorenzen, P. (1960). Logik und agon. In Atti Congr. Internat. di Filosofia, volume 4, pages 187–194, Sansoni, Firenze.
Łukasiewicz, J. (1920). Ologicetròjwartościowej. Ruch Filozoficzny, 5:169–171.
Metcalfe, G., Olivetti, N., and Gabbay, D. M. (2004). Analytic calculi for product logics. Archive for Mathematical Logic, 43(7):859–889.
Metcalfe, G., Olivetti, N., and Gabbay, D. M. (2005). Sequent and hypersequent calculi for Abelian and Łukasiewicz logics. To appear in ACM TOCL. Available at http://www.dcs.kcl.ac.uk/pg/metcalfe/.
Paris, J. (1997). A semantics for fuzzy logic. Soft Computing, 1:143–147.
Ruspini, E. H. (1991). On the semantics of fuzzy logic. International Journal of Approximate Reasoning, 5:45–88.
Varzi, A. (2001). Vagueness, logic, and ontology. The Dialogue, 1:135–154.
Weatherson, B. (2003). Many many problems. Philosophical Quarterly, 53:481–501.
Williamson, T. (1994). Vagueness. Routledge, London.
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
Fermüller, C.G. (2009). Revisiting Giles's Game. 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_9
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9374-6_9
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)