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Chapitre D'ouvrage Année : 2010

Some Remarks on Relations between Proofs and Games

Résumé

This paper aims at studying relations between proof systems and games in a given logic and at analyzing what can be the interest and limits of a game formulation as an alternative semantic framework for modelling proof search and also for understanding relations between logics. In this perspective, we firstly study proofs and games at an abstract level which is neither related to a particular logic nor adopts a specific focus on their relations. Then, in order to instantiate such an analysis, we describe a dialogue game for intu-itionistic logic and emphasize the adequateness between proofs and winning strategies in this game. Finally, we consider how games can be seen to provide an alternative formulation for proof search and we stress on the possible mix of logical rules and search strategies inside games rules. We conclude on the merits and limits of the game semantics as a tool for studying logics, validity in these logics and some relations between them. 2 Proofs and Games In this section, we present a common terminology to present both proof systems and games at a relatively abstract level. Our aim consists in obtaining tools on which bridges can be built between the proof-theoretical approach and the game semantics approach in establishing the (universal) validity of logical formulae. We explain how proofs and games can be viewed as complementary notions. We illustrate how proof trees in calculi correspond to winning strategies in games and vice-versa.
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Dates et versions

hal-00580302 , version 1 (27-03-2011)
hal-00580302 , version 2 (11-12-2015)

Identifiants

  • HAL Id : hal-00580302 , version 2

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Didier Galmiche, Dominique Larchey-Wendling, Joseph Vidal-Rosset. Some Remarks on Relations between Proofs and Games. Pierre Edouard Bour, Manuel Rebuschi, Laurent Rollet,. Construction - Festschrift for Gerhard Heinzmann, College Publications, 2010, 978-1-84890-016-5. ⟨hal-00580302v2⟩
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