So far we have spoken of truth at times or truth at worlds. But of course many interesting sentences in natural language are true or false with respect to both a time and a world. Thus, in place of (2) on p. 3 you would have

(1) ‘It is raining in Waitarere’ is true at a time t in a world w iff it is raining in Waitarere at t in w.

When both times and worlds are involved it is convenient to use the terminology of set theory, whereby, if w is a world and t is a time then 〈w,t〉 denotes the pair consisting of w and t in that order. So we may speak of a sentence α as true or false at a 〈w,t〉 pair, meaning simply that it is true (or false) in world w at time t.

Time and modality are intimately connected. A person situated in a world at a time may be deliberating what to do. An attractive way of modelling this deliberation is to imagine the ways in which things could develop from that time. One picture of time sees it as a single string of moments in a linear earlier/later relation. Then two ways things might develop could be represented by two such strings. Corresponding to sentence (2) in the Introduction (p. ix), we could have

(2) It might have been raining today in Waitarere.