Giles’s Game and the Proof Theory of Łukasiewicz Logic

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

Abstract

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.

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References found in this work

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

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