FROM GAMES TO DIALOGUES AND BACK Towards a general frame for validity
In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical Propositional logic and for classical First-order logic, an exact connection between 'intuitionistic dialogues with hypotheses' and semantical games is established. Various questions of a philosophical nature are also shown to arise as a result of the comparison, among them the relation between the model-theoretical and proof-theoretical approaches to the philosophy of logic and mathematics. 1. Introduction The fact that game-theoretical semantics (GTS) and dialogic are sisters has been widely acknowledged. The differences between the original approaches have been discussed too: while GTS relates to the study of truth in a model, dialogic has explored the possibilities of a certain type of proof-theoretical approach to validity. Despite the close relationship between the two approaches, no detailed, thorough analysis of their interaction has yet been undertaken. The insightful article of Saarinen (1978) is, however, a notable early attempt at a comparison of the two approaches. The aim of this paper is to present, from the viewpoint of * Partially supported by a personal grant from Finnish Cultural Foundation; and partially carried out within the project 207188 of the Academy of Finland. Work done in part at UMR Savoirs et Textes, Université Lille 3.