Our focus in this chapter is the semantics of tense, one of the main devices for encoding time in language. The grammatical category of tense is used to locate a situation or event in time, typically in interaction with aspect. When tense relates the speaker's temporal focus, what is normally called the reference time, to the speech time, we have deictic or absolute tense. Aspect, on the other hand, is concerned with the internal temporal structure of the event, for example, whether the event time is included or not in the reference time.
Tense is typically marked by verbal morphology, normally an affix on the matrix verb or on an auxiliary verb, but the semantic tense operator is not interpreted at the verb. The operator can be located quite distant from the verb at the level of logical form. Thus, we must distinguish between tense semantics and tense morphology.
We will assume that ourmodel contains a set of times I, and, furthermore, that verbs have a temporal argument of the semantic type i (time intervals). The latter assumption will be revised when we include aspect in the analysis. Times are partially ordered by the relations ≺ ‘before’ and ≻ ‘after’. Time intervals are coherent sets of time points. Hence, they may overlap, stand in the inclusion relation and so on (von Stechow, 2009b).
While everybody agrees that themeaning of past and future tenses is relational – with past placing the reference time before now and future after now – there is a long-standing issue in the literature as to the exact status of the reference time: is it quantificational or referential? We argue that this question cannot be answered straightforwardly. In our view, tenses, such as the simple past in English, are ambiguous between an indefinite (quantificational) and a definite (referential) interpretation of the reference time.
We will suggest that the data invite a dynamic account, according to which indefinite terms are analysed as introducing a new discourse marker (dm), whereas definite terms are considered to be anaphoric to an old dm and are in fact entirely presupposed.