Eventualities in Time

This paper addresses the general question of how eventualities should be localized in time. The more speciic question about the localization of states and events is discussed, too. For these questions the theory of tense and aspect in Discourse Representation Theory (DRT) is closely investigated, as far as relevant for single-sentence-discourses. The answers given here are mainly inspired by DRT as presented in KR93]. We show that the way eventualities are localized in time in that book contains some inconsistencies. In particular there is a mathematical problem concerning the localization function and a linguistic problem concerning the basic aspectual schema with culmination point. We propose a remedy for these problems. As main results we propose a change in the theory of aspect and a new deenition of an eventuality structure. The general picture that emerges should be interesting not only for DRT but for other theories using an eventuality-based semantics as well.