On Temporal Quantification

Abstract

Generally, it is assumed ever since Pratt & Francez (2001) that temporalexpressions have a context-dependent meaning in the sense that they notonly denote a set of time intervals according to their lexical content but rather their denotation is additionally restricted to some contextual time. Hence, Monday does not just denote the set of Mondays but a function from time intervals to the Mondays in them. This is useful in dealing with concomitant quantifiers such as John kissed Mary every second semester on every Monday for it allows them to restrict each other domain of quantification. In this paper I propose a way to eliminate this context dependency of temporal expressions building up on an idea of Irene Heim that domain restriction in the temporal domain is a matter of presupposition projection. In particular I argue that temporal prepositions presuppose that their argument, a time interval, intersects a higher time interval. This not only helps to derive concomitant quantification but also solves some classical problems of competing theories.