Preuves et jeux sémantiques

Philosophia Scientiae 8 (2):105-123 (2004)
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Abstract

Hintikka makes a distinction between two kinds of games: truthconstituting games and truth-seeking games. His well-known game-theoretical semantics for first-order classical logic and its independence-friendly extension belongs to the first class of games. In order to ground Hintikka’s claim that truth-constituting games are genuine verification and falsification games that make explicit the language games underlying the use of logical constants, it would be desirable to establish a substantial link between these two kinds of games. Adapting a result from Thierry Coquand, we propose such a link, based on a slight modification of Hintikka’s games, in which we allow backward playing for ∃loïse. In this new setting, it can be proven that sequent rules for first-order logic, including the cut rule, are admissible, in the sense that for each rule, there exists an algorithm which turns winning strategies for the premisses into a winning strategy for the conclusion. Thus, proofs, as results of truth-seeking games, can be seen

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Denis Bonnay
Université Paris Nanterre

Citations of this work

Between proof and truth.Julien Boyer & Gabriel Sandu - 2012 - Synthese 187 (3):821-832.
The Philosophy of Jaakko Hintikka.Paul Gochet - 2009 - Diogenes 56 (4):101-121.

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