Giles’s Game and the Proof Theory of Łukasiewicz Logic

Studia Logica 92 (1):27 - 61 (2009)

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.
Keywords dialogue games  Łukasiewicz logic  many-valued logics  hypersequents
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DOI 10.1007/s11225-009-9185-2
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References found in this work BETA

A Constructive Analysis of RM.Arnon Avron - 1987 - Journal of Symbolic Logic 52 (4):939 - 951.
Logik und Agon.Paul Lorenzen - 1960 - Atti Del XII Congresso Internazionale di Filosofia 4:187-194.
A Non-Classical Logic for Physics.Robin Giles - 1974 - Studia Logica 33 (4):397 - 415.

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Game-Theoretic Semantics for Non-Distributive Logics.Chrysafis Hartonas - 2019 - Logic Journal of the IGPL 27 (5):718-742.
Randomized Game Semantics for Semi-Fuzzy Quantifiers.C. G. Fermuller & C. Roschger - 2014 - Logic Journal of the IGPL 22 (3):413-439.

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