Dialogue games for many-valued logics -- an overview (Q1005947)

Among the few convincing approaches to the foundations of many-valued logics, in particular fuzzy logics, we find their Lorenzen-style characterisation on the basis of dialogue games. Intuitively, the idea is to define an idealised game between a proponent and an opponent of a formula in the course of which the formula and its constituents are questioned and defended; and to characterise logical validity by the existence of a winning strategy for the proponent. The present paper contains an overview over different versions of dialogue games for different logics. The starting point is Lorenzen's well-known game for intuitionistic logic, followed by a review of the game proposed by Giles, who in this way brought fuzzy logic, namely Łukasiewicz logic, into play. Then, several generalisations and modifications are discussed which are to a large part due to the author himself. We find, for instance, a game adequate for product logic and different types of games for Gödel logics. Furthermore, interval-based logics are addressed as well as SŁ, a common extension of S5 and Łukasiewicz logic.