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 modeling proof search and also for understanding relations between logics. In this perspective, we rstly study proofs and games at an abstract level which is neither related to a particular logic nor adopts a speci c focus on their relations. Then, in order to instantiate such an analysis, we describe a dialogue game for intuitionistic 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.