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.
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 in three papers:
In David Foster Wallace's novel Infinite Jest, the protagonist Hal Incandenza has written an essay entitled Montague Grammar and the Semantics of Physical Modality. Montague grammar is also referenced explicitly and implicitly several times throughout the book.
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