Rule ordering : A Look at Quantifier Scope and Coordination in GTS

Abstract

This article investigates a topic in game-theoretical semnatics (GTS) that has received relatively little attention in the previous literature: ordering principles that guide the application of game rules. Sentences with quantifier scope ambiguities show that ordering principles allow game rules to be played in different orders, which yields two or more different games for some input sentences. These distinct games correspond to distinct semantic interpretations. Based on datainvolving complex quantifier scope ambiguities, including inverse linking examples, a new ordering principle for quantifiers is proposed. It is argued that a hierarchy is needed that determines the relative precedence of ordering principles, and a partial hierarchy is presented towards that end. The approach is then tested with respect to coordination and quantifier scope.