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This paper addresses the general question of how eventualities should be localized in time. The answer given here is mainly inspired by the model theory of Discourse Representation Theory (DRT) as presented in Kamp and Reyle (1993). We show that there is a mathematical problem concerning the localization function used in that book. And we propose a remedy for this problem. The general picture that emerges should be interesting not only for DRT but for other theories using an eventuality-based semantics as well.

Eventualities in Time: The localization of eventualities in the Platonist and the Reductionist picture of time