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Stefano Aguzzoli & Agata Ciabattoni (2000). Finiteness in Infinite-Valued Łukasiewicz Logic.

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  1.  34
    Giles's Game and the Proof Theory of Łukasiewicz Logic.Christian G. Fermüller & George Metcalfe - 2009 - Studia Logica 92 (1):27 - 61.
    In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In (...)
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    Giles’s Game and the Proof Theory of Łukasiewicz Logic.Christian G. Fermüller & George Metcalfe - 2009 - Studia Logica 92 (1):27-61.
    In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ' disjunctive strategies' for Giles's game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. (...)
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