A Logical Framework for Dialogue Games

Logical validity and consequence are usually characterized either semantically by reference to models or syntactically via formal proof systems. However, already since the late 1950s Paul Lorenzen and his collaborators independently developed a third, pragmatic approach to logic, that identifies constructive validity with the existence of a winning strategy in a formal game where the proponent of a statement defends this statement against systematic attacks by an opponent. This dialogue game based paradigm has been extended to a wide range of logics since. However, so far almost all results refer to particular versions of dialogue games and treat different logics in a case by case manner. A central goal of this project is to provide a formal framework for logical dialogue games, that allows us to establish general results for a wide class of game variants and corresponding families of logics. In this endeavor we will employ the rich toolbox of modal logic that arose with the frequently mentioned "dynamic turn" of contemporary logic a development that explicitly addresses the challenges provided by the interactive nature of processing logically complex information by human as well as artificial agents. Moreover, we will draw on results and tools from argumentation theory, thus relating the dialogical approach to logic with insights from the wider realm of models of rational argumentation studied in Informal Logic and in Artificial Intelligence. On the other hand, we seek to highlight the relation between logical dialogues games and evaluation games (semantic games), as well as with analytic proof systems. Building on previous expertise in (fuzzy) logic based models of reasoning with vague information, we will finally apply our results to many-valued logics, in particular to fuzzy logics and their extensions with features inspired by contextualist theories of vagueness as e.g. developed by Stewart Shapiro.

The use of formal games in logic has a venerable tradition that gained in importance and visibility more recently. The project contributed to this stream of research by extending and analyzing the connection between two different types of logical games: on the one hand, dialogue games, originally introduced by Paul Lorenzen to characterize constructive reasoning; on the other hand, semantic games (also known as evaluation games), independently proposed by a number of researchers since the 1970s.The project lead to new instances of both types of games. Moreover, it has been established that the consideration of uniformly random moves, in addition to the moves by the two strategic players of a semantic game, greatly increases the expressive power for fixing the meaning of logical connectives and quantifiers. Further project results concern the relation between analytic proof systems and logical games. In particular, novel interpretations of logical rules in terms of so-called Client-Server games open up new directions for research.