Formal dialogue games are a traditional approach to characterize the semantics of logics. In the 1970s Robin Giles attempted to provide an operational foundation for formal reasoning in physical theories by dialogue games based on atomic experiments that may show dispersion. This thesis motivates, describes and analyzes his approach and the connection to t-norm based fuzzy logics. We give a short introduction into t-norms and many-valued logics based on t-norms. In particular we focus on three fundamental t-norm based fuzzy logics: Lukasiewicz Logic, Gödel Logic, and Product Logic. We present and discuss several approaches for extending the game rules of Giles’s Game in order to make it adequate for Gödel Logic and Product Logic. Moreover, we give hints at a strong correspondence between winning strategies in the game and derivations in an analytic proof system based on relational hypersequents. Another type of dialogue games are truth comparison games. This type is suitable for Gödel Logic and relates more to the degree based semantics of that logic than Giles’s Game. We present the game and discuss winning strategies for both players indicating the validity or refutability of a formula. Additionally, several utilities implemented in the context of this thesis are presented. Amongst these is a web-based application which allows for the interactive exploration of Giles’s Game and its extensions.
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