Studia Logica

, Volume 92, Issue 1, pp 27–61 | Cite as

Giles’s Game and the Proof Theory of Łukasiewicz Logic

  • Christian G. FermüllerEmail author
  • George Metcalfe


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.


dialogue games Łukasiewicz logic many-valued logics hypersequents 


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut für ComputersprachenTechnische Universität WienViennaAustria
  2. 2.Mathematics DepartmentVanderbilt UniversityNashvilleUSA

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