4 found
  1.  11
    Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach (1998). Labeled Calculi and Finite-Valued Logics. Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any finite-valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number (...)
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  2.  18
    Christian G. Fermüller & George Metcalfe (2009). Giles's Game and the Proof Theory of Łukasiewicz Logic. 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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  3.  5
    Christian G. Fermüller & Christoph Roschger (2014). From Games to Truth Functions: A Generalization of Giles's Game. Studia Logica 102 (2):389-410.
    Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Łukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for logical connectives with a scheme for betting on results of dispersive experiments for evaluating atomic propositions. We analyze this game and provide conditions on payoff functions that allow us to extract many-valued truth functions from dialogue rules of a quite general form. Besides finite and infinite valued Łukasiewicz logics, also (...)
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  4.  1
    Christian G. Fermüller (2009). Revisiting Giles's Game. In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag 209--227.
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