Giles's Game and the Proof Theory of Lukasiewicz Logic

摘要

In the 1970s, Robin Giles introduced a game combining Lorenzen-styledialogue rules with a simple scheme for betting on the truth of atomic statements, andshowed that the existence of winning strategies for the game corresponds to the validityof formulas in Lukasiewicz logic. In this paper, it is shown that 'disjunctive strategies'for Giles's game, combining ordinary strategies for all instances of the game played onthe same formula, may be interpreted as derivations in a corresponding proof system.In particular, such strategies mirror derivations in a hypersequent calculus developed inrecent work on the proof theory of Lukasiewicz logic.