Montague grammar

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Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on formal logic, especially lambda calculus and set theory, and makes use of the notions of intensional logic and type theory. Montague pioneered this approach in the 1960s and early 1970s.

Montague's thesis was that there is no essential difference between the semantics of natural languages (like English) and formal languages (like predicate logic). The central notions behind the Montague grammar were first proposed in the paper, "The Proper Treatment of Quantification in Ordinary English".

Montague's treatment of quantification has been linked to the notion of continuation in programming language semantics. (See Continuations in Natural Language.)

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[edit] Further reading

"The Proper Treatment of Quantification in Ordinary English", Richard Montague, reprinted in Formal Semantics: The Essential Readings, by Paul Portner, Barbara H. Partee,eds. Blackwell, 2002. ISBN 0631215425
Introduction to Montague Semantics by D.R. Dowty, R.E. Wall and S. Peters (Kluwer Academic Publishers, 1981) ISBN 9027711429
Informal Lectures on Formal Semantics by Emmon Bach (SUNY Press, 1989) ISBN 0887067719
Mathematical Methods in Linguistics by B.H. Partee, A.G.B. ter Meulen and R.E. Wall (Kluwer Academic Publishers, 1990) ISBN 9027722455
"Montague Grammar", by B.H. Partee with Herman Hendriks, in: Handbook of Logic and Language, eds. J.F.A.K. van Benthem and A.G.B. ter Meulen (Elsevier/MIT Press, 1997), pp.5-92. ISBN 0262220539