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	Montague grammar - Definition, explanation
		Montague grammar is an approach to natural language semantics, based on formal logic, especially lambda calculus and set theory.
		Montague grammar was named after American logician Richard Montague, who 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).
	www.calsky.com /lexikon/en/txt/m/mo/montague_grammar.php (167 words)

	Montague grammar - Wikipedia, the free encyclopedia
		Montague grammar is an approach to natural language semantics, based on formal logic, especially lambda calculus and set theory.
		Montague grammar was named after American logician Richard Montague, who 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).
	en.wikipedia.org /wiki/Montague_grammar (156 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		In Chapter 1, `Flexible Montague Grammar', it is argued that adoption of flexible type assignment in Montuage grammar leads to an elegant account of natural language scope ambiguities which arise in the pesence of quantifying and coordinating expressions.
		The proposal is formalized as a fully explicit fragment of flexible Montague grammar, which is shown to allow one to represent scope ambiguities without special syntactic or semantic devices and, thus, to involve a more adequate division of labour between the syntactic and semantic component.
		The flexible Montague grammar of Chapter 1 turns out to be compositional under the `most intuitive' interpretation of the principle, provided that the type-shifting derivation of translations is explicitly incorporated into the grammar.
	www.illc.uva.nl /Publications/Dissertations/DS-1993-05.abstract.txt (661 words)

	HANDBOOK OF LOGIC AND LANGUAGE, Elsevier Science, 1996, Introduction Chapter 1 (Site not responding. Last check: 2007-10-15)
		``Montague grammar'' is a term that was first applied soon after the untimely death of Richard Montague (September 20, 1930 -- March 7, 1971) to an approach to the syntax and semantics of natural languages based on Montague's last three papers (Montague, 1970b, 1970c, 1973).
		In its narrower sense, ``Montague grammar'', or ``MG'', means Montague's theory and those extensions and applications of it which remain consistent with most of the principles of that theory.
		The plan of this article is to highlight the historical development of Montague grammar as both narrowly and broadly construed, with particular attention to the key ideas that led Montague's work to have such a great impact on subsequent developments.
	www.elsevier.com /homepage/sac/hll/prefch1.htm (351 words)

	logicandlanguage.net: Montague Intrigue
		I decided that I wanted to know more about Montague grammar, in part because I have always been curious about Montague and his work, and in part because I have a hunch that it might help me with the chapter...
		I decided that I wanted to know more about Montague grammar, in part because I have always been curious about Montague and his work, and in part because I have a hunch that it might help me with the chapter I am writing.
		Montague and Solomon Feferman were both PhD students of Tarski around the same time (the 1950s), so the Fs' description of his frenetic life is first-hand reporting.
	www.logicandlanguage.net /archives/2005/05/montague_intrig.html (1503 words)

	Lojban Wiki : Montagovian (Site not responding. Last check: 2007-10-15)
		I did indeed, and during the time that he was developing Montague Grammar, which is probably the main reason to be interested in him.
		Montague added a transformational component, so that to work the two pieces did not have to occur next to each other in the surface structure of the text.
		The cancellation grammar lends itself nicely to Frege's sort of semantics — things with holes in them are of a class with labelled holes.
	www.lojban.org /tiki/tiki-print.php?page=Montagovian (241 words)

	Montague grammar -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-15)
		Montague grammar is an approach to (A human written or spoken language used by a community; opposed to e.g.
		Montague's thesis was that there is no essential difference between the semantics of natural languages (like (An Indo-European language belonging to the West Germanic branch; the official language of Britain and the United States and most of the Commonwealth countries) English) and formal languages (like (additional info and facts about predicate logic) predicate logic).
		Montague's treatment of (The act of discovering or expressing the quantity of something) quantification has been linked to the notion of (The act of continuing an activity without interruption) continuation
	www.absoluteastronomy.com /encyclopedia/m/mo/montague_grammar.htm (265 words)

	Concepts in the Lexicon: Part I
		The grammar of a language can be reduced to relatively simple rules that show what categories of words may occur on the right or the left of a given word (the Schankian expectations or the cancellation rules of Montague grammar).
		Montague's representations were lambda expressions, which have the associated operations of function application, lambda expansion, and lambda contraction.
		To allow greater flexibility, some of Montague's rigid constraints must be relaxed: his requirement of a strict one-to-one mapping between syntactic rules and semantic rules; his use of lambda expressions as the primary meaning representation; and his inability to handle ellipsis, metaphor, metonymy, anaphora, and anything requiring background knowledge.
	www.jfsowa.com /ontology/lex1.htm (8070 words)

	HANDBOOK OF LOGIC AND LANGUAGE, Elsevier Science, 1996, Introduction Chapter 12 (Site not responding. Last check: 2007-10-15)
		Ironically, the combinatorial apparatus of Generative Grammar with its focusing on derivations of syntactic structures on the basis of grammatical rules was methodologically closer to logical deductive systems than the descriptive approach of Montague Grammar.
		Thus, semantic structures in the sense of Montague Grammar, being certain interpreted lambda-terms, can also be regarded as formal derivations of linguistic expressions on the basis of a logical grammar whose rules are fashioned according to the Natural Deduction format.
		Grammars are represented by Prolog programs, and grammatical derivations are simulated by executions of these programs, that means, logical proofs employing resolution and unification (see Pereira and Shieber, 1987; Gazdar and Mellish, 1989).
	www.elsevier.com /homepage/sac/hll/prefch12.htm (1501 words)

	Hartwell Abridged (Site not responding. Last check: 2007-10-15)
		Those who defend the teaching of grammar tend to have a model of composition instruction that is rigidly skills-centered and rigidly sequential: the formal teaching of grammar, as the first step in that sequence, is the cornerstone or linchpin.
		The first thing we mean by "grammar" is "the set of formal patterns in which the words of a language are arranged in order to convey larger meanings." It is not necessary that we be able to discuss these patterns self-consciously in order to be able to use them.
		Actually, the form of Grammar 2 which is usually taught is a very inaccurate and misleading analysis of the facts of Grammar 1; and it therefore is of highly questionable value in improving a person's ability to handle the structural patterns of his language.
	www.suu.edu /faculty/simon/2710/hartwell.html (4527 words)

	Berkeley Construction Grammar
		Construction Grammar (CG) is a non-modular, generative, non-derivational, monostratal, unification-based grammatical approach, which aims at full coverage of the facts of any language under study without loss of linguistic generalizations, within and across languages.
		CG adopts from traditional grammar the idea that a grammar is composed of conventional associations of form and meaning, that is, grammatical constructions.
		Among current non-modular approaches to grammar, CG places great emphasis on the fact that probably any of the kinds of information that have been called 'pragmatic' by linguists may be conventionally associated with a particular linguistic form and therefore constitute part of a rule (construction) of a grammar.
	www.icsi.berkeley.edu /~kay/bcg/bcg/cg_define.html (2686 words)

	Mathématiques & Sciences Humaines - Mathematics and Social Science
		The implementation covers the fundamental operations of Montague’s PTQ model: the construction of analysis trees, the linearization of trees into strings, and the interpretation of trees as logical formulas.
		Moreover, a parsing algorithm is derived from the grammar.
		To this end, a version of Montague grammar is developed, with syntactic categories relativized to a context and to domains of individuals.
	www.ehess.fr /revue-msh/recherche_gb.php?auteur=126 (498 words)

	A Farewell to Logic in Action: Hans Kamp
		When in the second half of the sixties Montague succeeded in applying the methods of model theory to significant fragments of natural language, this came as a great surprise to the community; until then almost everyone had been convinced that natural languages were far too "organic" and unsystematic to permit analyses of this sort.
		Montague himself emphasised his diverging opinion by stating that there were no significant differences between natural languages and the languages of formal logic.
		This emerging picture of a multiplicity of different forms of information representation suggests a conception of logic that is very different from the one that was prevalent in the early days of Montague Grammar, and, in fact which is still the view espoused by many today.
	www.illc.uva.nl /lia/farewell_kamp.html (2103 words)

	The formal approach to meaning
		Montague's papers are highly formal and condensed, very difficult for ordinary humans (even logicians!) to read with comprehension.
		Montague's aim was not to construct a grammar for the whole language, but rather to give a complete (and completely explicit) syntax and semantics for an infinite subpart of the language which contained some constructions which pose interesting challenges for the semantician.
		Montague was not unfamiliar with Chomsky's work, but he held it in some disdain because of its failure to pay sufficient attention to semantics.
	www.msu.edu /user/abbottb/formal.htm (7353 words)

	Chaotic Logic: Chapter Five - Linguistic Systems
		A Montague grammar is a transformation system, in the sense defined above -- the transformation rules are the "syntactic operations," and the initials are the "basic expressions." But it is a very special kind of transformation system.
		Montague assumes that there is one big situation, in which everything applies; but his axioms could be "situated" without too much difficulty (by modifying 1, 4 and 6).
		Montague believed that the most important aspects of semantics could be developed in a purely formal way, and that considerations of content, being somehow more superficial, could be tacked on afterwards.
	goertzel.org /books/logic/chapter_five.htm (10095 words)

	The Montague Corner (Site not responding. Last check: 2007-10-15)
		Richard Montague is one of the most well-known logical grammarians of the past decades.
		I knew Montague personally from a course I followed in 1966 or 1967 in Amsterdam (jointly given by Frits Staal and Montague), so I recalled him, with glasses, and somewhat older.
		It's not so much that I want to make a shrine, but on the other hand it is amazing that Montague was dealt with so abstractly as to make him invisible, although Johan van Benthem observes that this trait could explain a lot about his influence.
	www.let.uu.nl /~Henk.Verkuyl/rm/montague.html (207 words)

	Theories with little or no syntax-semantics mismatches:
		Various architectures of grammar differ with regard to whether they are philosophically at ease with the existence of significant mismatches between syntactic and semantic form.
		Thus Montague 1970 went on record as committed to the idea that the grammatical organization of sentences could be taken as a sufficient representation of the logic of the sentences with no modification whatsoever, though most implementations of Montague's ideas in fact contain, for convenience, rules of translation, usually accompanied with apologies.
		Finally, there are at least two views of how grammar ought to operate that radically segregate the representational levels, deriving each according to its own units and principles with complete, or near-complete disregard for what is going on in the other levels.
	csli-publications.stanford.edu /LFG/5/bfg00/bfg00sadock.html (2621 words)

	Beschrijving 200501052 (Site not responding. Last check: 2007-10-15)
		Most current research in formal semantics for natural language is based on the framework known as “Montague Grammar”, developed from the seminal work of Richard Montegue in the early seventies.
		Students will familiarize themselves with the technical apparatus used in Montague Grammar but the focus will be on linguistic issues and the treatment of quantification, intensionality and variable binding.
		The purpose of this course is to provide the student of linguistics with sufficient knowledge of the foundations of formal semantics to allow her/him to read current research literature on the topic.
	www2.let.uu.nl /cursuskrant/descriptionMaEng.asp?year=2005&id=200501052 (140 words)

	DEEP LANGUAGE - The New York Review of Books
		Chomsky always cites examples of putative universals from transformational grammar, but the fact is that just about every other theory of grammar that has ever been seriously proposed has, either implicitly or explicitly, incorporated claims for extremely complex and sophisticated linguistic universals.
		Chomsky appears not to have read this Latin grammar (an English translation of which was in Widener Library) but Robin Lakoff studied it and published her findings in the review mentioned in footnote 1.
		The really deep results of transformational grammar are, in my opinion, the negative ones, the hosts of cases where transformational grammar fell apart for a deep reason: it tried to study the structure of language without taking into account the fact that language is used by human beings to communicate in a social context.
	www.nybooks.com /articles/9956 (1680 words)

	ipedia.com: Richard Montague Article (Site not responding. Last check: 2007-10-15)
		His research focused on the foundations of logic and set theory, and pioneered a logical approach to natural language semantics which be...
		Richard Montague (1930–1971) was an American mathematician and philosopher.
		His research focused on the foundations of logic and set theory, and pioneered a logical approach to natural language semantics which became known as Montague grammar.
	www.ipedia.com /richard_montague.html (128 words)

	Montague Grammar
		Montague said: "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 languages within a single natural and mathematically precise theory."
		I learned it stepwise, from traditional propositional logic, predicate logic, two-sorted logic, modal logic, tense logic, type theory, categorial grammar, intensional logic (they all are simple systems of formal language, so it's not difficult at all to acquire them).
		Frege's predicate logic is a more powerful language system, and Montague Grammar is a much more productive paradigm which can give a semantics for natural language.
	www.englishforums.com /English/MontagueGrammar/bvzpz/Post.htm#104878 (1345 words)

	Chomskyan versus Formalist Linguistics
		The titles of this parasession and of Newmeyer's (1998) book suggest that the principal dividing line between opposing approaches in linguistics is the one between functionalist and formalist approaches.
		However, treating the opposition between GPSG and Chomskyan linguistics as internal to generative grammar (or to formalist approaches to linguistics) is misleading.
		Ten Hacken (2000) shows that it is impossible in principle to construct a model of the research programme underlying GPSG and Montague semantics in a way parallel to the one for Chomskyan linguistics.
	pages.unibas.ch /LIlab/staff/tenhacken/cls37 (594 words)

	[No title]
		This led to the view that as far as natural languages were concerned logical analysis was a matter of rendering sentences of the language in some antecedently defined logical (or formal) language, where the relation between the sentences in the languages is to be specified by some sort of contextual definition or rules of translation.
		Montague, R. (1974) The Proper Treatment of Quantification in Ordinary English.
		Partee, B. (1975) Montague Grammar and Trasnformational grammar.
	kleene.ss.uci.edu /~rmay/LogicalForm.html (1317 words)

	Mark "Monty" Montague
		There is a Montague expressway in the middle of silicon valley, tho, a Montague Art Galllery (which has some pretty neat stuff), and a Folding Bicycle Company.
		A Mark Montague who is not me, but is closer than most, has an abstraction which is not a web page.
		I'm not the other Mark Montague in Pasadena, even though I got a summons for him once, and I have proven that my eyesight is considerably different than his, to the consternation of our mutual optician.
	www.gg.caltech.edu /~monty/monty.shtml (2350 words)

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