In this paper, we point out that past time operators (PTOs) in Luganda, a language that makes three past time remoteness distinctions, are vague and context-dependent, and pro- vide an analysis whereby PTOs contain context-sensitive measure functions akin to gradable adjectives. We call the relevant PTOs RECENT, INTERMEDIATE, and DISTANT, respectively. Luganda PTOs give rise to borderline cases, where it is difficult to decide whether a past reference time (RT) counts as ‘recent’, ‘intermediate’ or ‘distant’. What counts as ‘recent’, ‘intermediate’ or ‘distant’ is context dependent; e.g., there are contexts where REC is acceptable with an RT of a few weeks ago, and contexts where DIST is acceptable for an RT of a few minutes ago. We assume that like tenses in English, PTOs in matrix clauses in Luganda restrict the relation between utterance time (UT) and RT. However, while English past tense presupposes that RT precedes UT (e.g. Kratzer 1998), Luganda PTOs additionally encode as part of their meaning a vague, context-dependent measure function that compares the length of a time interval to a contextual standard.

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