Lorenzen's Games and Linear Logic

This paper presents some basic notions concerning Lorenzen's game tra-dition and its relation with Linear Logic. It is shown that Lorenzen's idea was applied in Blass ' work in order to dene a game semantics for Linear Logic. Originally Blass came-up with these ideas on 70's, however they were fully developed only in 1992. Moreover, by identifying the source of the problems in Blass ' approach, Abramsky developed a system using the same pattern of games for which Linear Logic is sound and complete. These systems are both exposed in the following text. Finally, some fur-ther issues are discussed and an alternative (and intuitive) approach is built in order to achieve the desired semantics taking into account nite games instead of innite. 1 1 Lorenzen's Game Semantics Each logic has a syntactical aspect (which denes the well-formed constructions