What criteria are sufficient for precision in formal semantics?

Question

For example:

A) "I have finished dinner, so I'm not hungry."

B) "I have read long books, so I can read this one."

One could say the function of "have" in these sentences is to communicate that the past actions result in current/future states.

But "result" can be more precisely broken into some direct effect as in A, and an evidence of ability as in B.

Is there a system one could use to do this to any concept? How does one know in what ways a concept needs to be broken down to be precise? And how deep must one go to be considered precise? How does one know when a concept is precise enough to do be formal and non-ambiguous?

Answer 1

We can model it with expressions like "for some X, if x has read long books then x can read this book".

So we can model the truth conditions of what you mean in English. But to model precisely the kind of dependency of past tense actions to future tense ones, I don't think we can do that in a semantics based on classical logic. All we can do is match the antecedent and the consequent's truth together. For example, when I say U: "If United score, they'll win", I have in mind a sense of "because"; I'm saying it's true because, for example, there's not much time left, or whatever. But logically, the sentence is still true if United score, get scored against, and then score again, even though, had i know united would be scored against after scoring, i wouldn't have thought "If united score, they'll win" was true.

Maybe the connection between consequent and and antecedent can be modelled better if we think that U is uttered under the assumption of implicit premises, and so so a short hand for every antecedent i have in mind, and when they're all satisfied, that models "because". Or maybe "because" is still there, a concept over and above the correspondence of truth between antecedent and consequent, and maybe some non classical logic (I'm not well versed in them I'm afraid) captures this I don't know.

It's an interesting question

Answer 2

Within Montague semantics there is a by now standard treatment of the present perfect due to David Dowty. According to this 'extended now semantics' the present perfect presupposes an 'extended now', a time interval, that includes the utterance time as a final subinterval and locates an event or state described by the sentence within the extended interval.

Formally this can be spelled out as follows: Let a temporal interval, I, be a closed, bounded, non-empty subset of the real line. For some fragment of a higher-order modal logical language (take e.g. Montague's IL without the up- and down-operators) we can define what it means that a formula A is true at a temporal interval.

We can enrich the language with a 1-place modal operator PRES-PERF, whose semantics is as follows:

(D) [PRES-PERF] A is true at interval I iff there is some interval J such that I is a proper final subinterval of J and there is another subinterval K of I such that A is true at K.

According to this semantics (A) (or its translation) is true in some interval I, if I is a final subinterval of J, properly contained in J, and for some subinterval K of J the sentence 'I finish dinner' is true at J. So, under this interpretation, the event of having dinner was completed at interval K and so is completed at the utterance time I. So, at the utterance time the conditions for not being hungry are satisfied.