Is there a book or text that tries to give an analysis of statements whose truth values are time-dependent. For example, a statement like "It is raining today" changes in truth value over time.
Yes I think so.
"Strictly speaking, what admit of truth and falsity are NOT statements as repeatable patterns of utterance, but individual events of statement utterance". Emphasis mine.
"The crucial point of contact between description and reality is to be sought in the utterance of a statement on the occasion of a stimulation to which that string of words has become associated."
Both from Pg. 1, Quine, Methods of Logic, 4th ed. (Harvard Press, 1982).
This answers your question I think, though it may not seem to do so. How would you measure changing truth value over time with anything less than a series of individual events of statement utterances based upon individual occasions of stimulation? (Very loosely speaking, at logic-level we are digitized,0101001 e.g. etc, not analog).