Abstract
Connections between games and logic are quite common in the literature: for example, to every analytic proof system with the subformula property (hence admitting cut-elimination) one can associate a game in which a player tries to find a cut-free proof and his opponent can attack parts of the proof constructed since then. Along these lines, formulas correspond to games and proofs correspond to winning strategies. A first connection between many-valued logic and games was discovered by Giles in [9]. A variant of such semantics was used in [4] in order to obtain a uniform proof system with a game-theoretical interpretation for Łukasiewicz, product and Gödel logics. The above mentioned papers are extremely interesting, but we would say that the interest of this game semantics is more proof-theoretical than game-theoretical.
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References
Blok, W.J., Ferreirim, I.M.A.: On the structure of hoops. Algebra Universalis 43, 233–257 (2000)
Blok, W.J., Pigozzi, D.: Algebraizable Logics. Mem. Amer. Math. Soc., 396, vol.77, Amer. Math. Soc., Providence (1989)
Burris, S., Sankappanavar, H.P.: A course in Universal Algebra. Graduate texts in Mathematics. Springer, Heidelberg (1981)
Ciabattoni, A., Fermüller, C., Metcalfe, G.: Uniform Rules and Dialogue Games for Fuzzy Logics. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 496–510. Springer, Heidelberg (2005)
Cicalese, F., Mundici, D.: Recent developements of feedback coding, and its relations with many-valued logic. In: van Benthem, J., Parikh, R., Ramanujam, R., Gupta, A. (eds.) FICL 2005. Proceedings of the First Indian Conference on Logic and its Applications, Bombay, India, January 2005 (to appear)
Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic foundations of many-valued reasoning. Kluwer, Dordrecht (2000)
Cignoli, R., Torrens, A.: An algebraic analysis of product logic. Mult. Val. Logic 5, 45–65 (2000)
Ferreirim, I.M.A.: On varieties and quasi varieties of hoops and their reducts, PhD thesis, University of Illinois at Chicago (1992)
Giles, R.: A non-classical logic for phisics. Studia Logica 4(33), 399–417 (1974)
Esteva, F., Godo, L., Hájek, P., Montagna, F.: Hoops and fuzzy logic. Journal of Logic and Computation 13, 531–555 (2003)
Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic-Studia Logica Library, vol. 4. Kluwer Academic Publ., Dordercht (1998)
Jipsen, P., Tsinakis, C.: A survey on residuated lattices. In: Martinez, J. (ed.) Ordered Algebraic structures, pp. 19–56. Kluwer, Dordrecht (2002)
Marini, C., Montagna, F., Simi, G.: Product logic and probabilistic Rényi-Ulam games. In: Fuzzy Sets and Systems (preprint 2005, to appear)
Mundici, D.: The logic of Ulam’s game with lies. In: Knowledge, Belief and Strategic Interaction, Cambridge Studies in Probability, Induction, and Decision Theory, pp. 275–284 (1992)
Pelc, A.: Searching with known error probability. Theoretical Computer Science 63, 185–202 (1989)
Pelc, A.: Searching games with errors - fifty years of coping with liars. Theoretical Computer Science 270, 71–109 (2002)
Rényi, A.: Napló az információelméletről, Gondolat, Budapest (1976) (English translation: A diary on Information Theory. J. Wiley and Sons, New York (1984))
Ulam, S.M.: Adventures of a Mathematician. Scribner’s, New York (1976)
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Jenei, S., Montagna, F. (2007). Rényi-Ulam Game Semantics for Product Logic and for the Logic of Cancellative Hoops. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds) Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science(), vol 4460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75939-3_14
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