Analyzing fuzzy and contextual approaches to vagueness by semantic games

How can natural language be ‘understood’ by computers? Or, more specifically, how can the semantics of a natural language statement be modeled by means of logic in order to facilitate formal reasoning? This perennial problem has many, partly intertwined facets; one of them being the pervasiveness of vagueness in all natural languages. Originally discarded by Frege as a ‘defect’ of ordinary language outside the scope of logic, vagueness nowadays has given rise to a multitude of approaches within logics, analytic philosophy, and linguistics. In this thesis we aim to shed some new light on (i) how to justify certain models of vagueness by means of game-theoretic semantics and (ii) how such different approaches to vagueness can be related to each other. Fuzzy logic is sometimes refered to as the ‘logic of vagueness’. There are several ways to attach a suitable semantics to fuzzy logics; particularly Giles’s semantic game for Lukasiewicz logic provides a game-theoretic semantics for this so-called t-norm based fuzzy logic. However none of these approaches has yet been extended to (semi-)fuzzy quantification. By introducing the notion of random witness selection we show how certain proportional semi-fuzzy quantifiers can be characterized within an extension of Giles’s game. We also provide a game-based characterization of Stewart Shapiro’s contextual account of vagueness in the tradition of Giles’s game by introducing a third player called Nature. We pick out Chris Barker’s account of ‘The Dynamics of Vagueness’ as a representative for a scale-(or degree-)based linguistic approaches to vagueness. First, we show how t-norm based fuzzy logics can be recovered from Barker’s account by measuring contexts. Although context sizes change in a non truthfunctional manner, t-norms and co-t-norms emerge as limit cases. We also investigate the delineation-based approach by the philosopher Stewart Shapiro. Both Barker’s and Shapiro’s approaches describe how context changes and evolves during a conversation, albeit by different means. We examine which kind of situations can be modeled in either of these approaches making the same assumptions and precisify what exactly it means for two models ‘to make the same assumptions’. We observe how context updates proceed in both models for a series of vague statements. As it turns out, the resulting models using both approaches give rise to exactly the same first-order inferences under certain conditions.