Some Remarks on Relations between Proofs and Games

International audienceThis 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

Préface

Ce numéro spécial, édité à l’occasion du centenaire de la naissance d’Alan Turing, est le fruit d’une double collaboration : d’une part une collaboration internationale qui exprime via internet l’importance de l’année Turing, d’autre part une collaboration locale régulière entre des chercheurs de l’équipe TYPES du Laboratoire Lorrain de Recherche en Informatique (LORIA) qui s’intéressent à la logique, la théorie de la preuve et la programmation, et des philosophes et logiciens du Laboratoire ..

Préface

Ce numéro spécial, édité à l’occasion du centenaire de la naissance d’Alan Turing, est le fruit d’une double collaboration : d’une part une collaboration internationale qui exprime via internet l’importance de l’année Turing, d’autre part une collaboration locale régulière entre des chercheurs de l’équipe TYPES du Laboratoire Lorrain de Recherche en Informatique (LORIA) qui s’intéressent à la logique, la théorie de la preuve et la programmation, et des philosophes et logiciens du Laboratoire ..

Contribution of high energy physics techniques to the medical imaging field

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Pericyte-Like Progenitors Show High Immaturity and Engraftment Potential as Compared with Mesenchymal Stem Cells

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