Montague grammar

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

Montague's thesis was that natural languages (like English) and formal languages (like programming languages) can be treated in the same way. "There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and mathematically precise theory. On this point I differ from a number of philosophers, but agree, I believe, with Chomsky and his associates." (Universal Grammar 1970)

Montague published what soon became known as Montague grammar^[1] in three seminal papers:

• 1970: "Universal grammar" (= UG)^[2]
• 1970: "English as a Formal Language" (= EFL)^[3]
• 1973: "The Proper Treatment of Quantification in Ordinary English" (= PTQ)^[4]

Montague's treatment of quantification has been linked to the notion of continuation in programming language semantics.^[5]

See also

• Categorial grammar
• Situation semantics
• Kripke semantics

References

1. ^ The linguist Barbara Partee credibly claims to have invented the term in 1971 “for the system spelled out in Montague's“ UG, EFL and “especially in PTQ”. See her essay "Reflections of a Formal Semanticist as of Feb 2005", p. 14, footnote 36.
2. ^ "Universal grammar". Theoria 36 (1970), 373–398. (reprinted in Thomason, 1974)
3. ^ "English as a Formal Language". In: Bruno Visentini (ed.): Linguaggi nella società e nella tecnica. Mailand 1970, 189–223. (reprinted in Thomason, 1974)
4. ^ "The Proper Treatment of Quantification in Ordinary English". In: Jaakko Hintikka, Julius Moravcsik, Patrick Suppes (eds.): Approaches to Natural Language. Dordrecht 1973, 221–242. (reprinted in Thomason, 1974)
5. ^ See Continuations in Natural Language

Further reading

• Richmond Thomason (ed.): Formal Philosophy. Selected Papers by Richard Montague. New Haven, 1974, ISBN 0300024126
• Paul Portner, Barbara H. Partee (eds.): Formal Semantics: The Essential Readings, Blackwell, 2002. ISBN 0631215425
• D.R. Dowty, R.E. Wall and S. Peters: Introduction to Montague Semantics. Kluwer Academic Publishers, 1981, ISBN 9027711429
• Emmon Bach: Informal Lectures on Formal Semantics. SUNY Press, 1989, ISBN 0887067719
• B.H. Partee, A.G.B. ter Meulen and R.E. Wall: Mathematical Methods in Linguistics. Kluwer Academic Publishers, 1990, ISBN 9027722455
• B.H. Partee with Herman Hendriks: Montague Grammar. 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

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