Dialogue game semantics for fuzzy logics

Vagueness is a ubiquitous and pervasive phenomenon in information processing. Most experts agree that modeling vagueness triggers reference to degrees of truth. Fuzzy Logics are based on the extension of the two classical truth values by infinitely many intermediary degrees of truth. So far formal deduction systems for specific fuzzy logics are hardly ever explicitly related to models of correct reasoning with vague information. We address the challenge to derive inference systems for fuzzy logics from first principles about approximate reasoning by a method that refers to important early results by Robin Giles. Giles combined a version of Paul Lorenzen`s strategic dialogue game with bets on the results of atomic experiments that may show dispersion, in an attempt to provide an operational foundation for formal reasoning in physical theories. He proved that the propositions that a player can bet on without expecting loss, coincide with those that are valid in Lukasiewicz logic, one of three fundamental, so-called t-norm based fuzzy logics. Giles`s remarkable result can, with hindsight, be seen as one of the few attempts to solve a fundamental problem in approximate reasoning: How to derive a `fuzzy logic` from first principles. We argue that Lorenzen/Giles-style dialogue games provide a general key for connecting proof systems with semantic models of approximate reasoning. The mentioned results merely provide a starting point for a systematic investigation of analytic systems and dialogue games as a semantic foundation of reasoning with vague notions. We tackle the outlined research programme via a list of rather concrete research aims, which can be categorized as follows: - Design of analytic systems and dialogue games. - Investigation of variations of Giles`s game. - Connecting game based semantics of fuzzy logic and theories of vagueness. Moreover, we implement a web-based tool that allows the exploration of various relevant dialogue games in action.

Vagueness is a ubiquitous and pervasive phenomenon in information processing. Most experts agree that modeling vagueness triggers reference to degrees of truth. Fuzzy Logics are based on the extension of the two classical truth values by infinitely many intermediary degrees of truth. So far formal deduction systems for specific fuzzy logics are hardly ever explicitly related to models of correct reasoning with vague information. We address the challenge to derive inference systems for fuzzy logics from first principles about approximate reasoning by a method that refers to important early results by Robin Giles. Giles combined a version of Paul Lorenzen`s strategic dialogue game with bets on the results of atomic experiments that may show dispersion, in an attempt to provide an operational foundation for formal reasoning in physical theories. He proved that the propositions that a player can bet on without expecting loss, coincide with those that are valid in Lukasiewicz logic, one of three fundamental, so-called t-norm based fuzzy logics. Giles`s remarkable result can, with hindsight, be seen as one of the few attempts to solve a fundamental problem in approximate reasoning: How to derive a `fuzzy logic` from first principles. We argue that Lorenzen/Giles-style dialogue games provide a general key for connecting proof systems with semantic models of approximate reasoning. The mentioned results merely provide a starting point for a systematic investigation of analytic systems and dialogue games as a semantic foundation of reasoning with vague notions. We tackle the outlined research programme via a list of rather concrete research aims, which can be categorized as follows: Design of analytic systems and dialogue games. Investigation of variations of Giles`s game. Connecting game based semantics of fuzzy logic and theories of vagueness. Moreover, we implement a web-based tool that allows the exploration of various relevant dialogue games in action.