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C. G. Fermüller 《Studia Logica》2008,90(1):43-68
An overview of different versions and applications of Lorenzen’s dialogue game approach to the foundations of logic, here largely restricted to the realm of manyvalued logics, is presented. Among the reviewed concepts and results are Giles’s characterization of ?ukasiewicz logic and some of its generalizations to other fuzzy logics, including interval based logics, a parallel version of Lorenzen’s game for intuitionistic logic that is adequate for finite- and infinite-valued Gödel logics, and a truth comparison game for infinite-valued Gödel logic. 相似文献
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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 particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the
proof theory of Łukasiewicz logic.
Presented by Daniele Mundici 相似文献
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Multiplicative Conjunction as an Extensional Conjunction 总被引:1,自引:0,他引:1
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