Montague Grammar is a cover term for the kind of syntactic and semantic work that is directly inspired by the work of the American philosopher Richard Montague. It is based on the idea that the meaning theories for natural languages and formal languages can and should be based on the same principles, according to a Universal Grammar, of which the Compositionality Principle is the most important one.
The clearest and most influential concrete illustration of Montague's ideas can be found in his article 'The Proper Treatment of Quantification in Ordinary English' (usually referred to as PTQ) in which he defined the syntax and semantics of a considerable fragment of English. The system of rules and notations given there are the point of departure for Montague Grammar. In PTQ, Montague does not interpret expressions of English directly, but he translates English words and phrases into expressions of a logical language IL which are interpreted in the usual model-theoretic way. PTQ employs some of the most advanced logical instruments: the sentences of English are generated by a categorial grammar, the syntactic counterpart of type logic, the logical language IL is a combination of intensional logic and type logic with lambda-abstraction which is interpreted relative to a model containing possible worlds and moments of time, and crucial use is made of #meaning postulates. The range of constructions and phenomena treated in PTQ includes quantifier scope, opaque contexts, conjunction, infinitival complements and relative clauses.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
- Montague, R. 1974. Formal philosophy: selected papers of Richard Montague, edited and with an introduction by Richmond H. Thomason, Yale University Press, New Haven