The mapping between the grammatical tenses of a natural language and the expression of temporal location is very complex, and one of the goals of linguistic semantics is to investigate the relation between grammatical tenses and the expression of time. To achieve this goal, scholars in both linguistics and philosophy have proposed different theories of tense.
One type of theory, beginning with the work of the logician Arthur Prior, analyzes tenses as temporal operators. Prior (1957, 1967) treated the past and future tenses as sentential operators meaning "it was the case that" and "it will be the case that," respectively. The sentence "Bill called" is translated into P(^p) and is true in a world w at a time t if and only if "Bill calls" is true in w at a time t′ t (^p is the intension of p, and "〈" means "earlier than"). In his intensional system, Montague (1974) adopted Prior's tense logic by introducing tense operators for the past and future tenses, with the time parameter of the intensional expression embedded in the tense operator.
A different approach to the analysis of tense is that proposed by Reichenbach (1947).
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