It was developed by the Polish logician Alfred Tarski (1902-1983), and applied to language by British philosopher Donald Davidson. (Also see: MONTAGUE GRAMMAR.)
Semantic theory for sentences rather than words (also see: LEXICAL SEMANTICS). We know the meaning of a sentence if we know the conditions under which it would be true.
The basic idea is that a sentence like 'Snow is white' is true in English (and 'Laneige est blanche' is true in French) if and only if snow is white. Truth is thus relative to a language, and Tarski applies the theory primarily to certain formal languages, developed so as to deal with the 'liar' paradox (is 'I am now lying' true or false?).
For this and other reasons the full statement of the theory is very complicated, which is itself one of the objections to it.
M Black, 'The Semantic Definition of Truth', Analysis (1948); reprinted in M Black, Language and Philosophy (1949), and in M Macdonald, ed., Philosophy and Analysis (1954);
R Kempson, Semantic Thought (Cambridge, 1977)