Montague grammar
Encyclopedia
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 language
s (like English
) and formal language
s (like programming language
s) 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 in three seminal papers:
Montague's treatment of quantification
has been linked to the notion of continuation
in programming language
semantics
.
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
, named after American logician Richard Montague
Richard Montague
Richard Merett Montague was an American mathematician and philosopher.-Career:At the University of California, Berkeley, Montague earned an B.A. in Philosophy in 1950, an M.A. in Mathematics in 1953, and a Ph.D. in Philosophy 1957, the latter under the direction of the mathematician and logician...
. The Montague grammar is based on formal logic
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
, especially higher order predicate logic
Predicate logic
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified...
and lambda calculus
Lambda calculus
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. The portion of lambda calculus relevant to computation is now called the untyped lambda calculus...
, and makes use of the notions of intensional logic
Intensional logic
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe , by additional quantifiers that range over terms that may have such individuals as their value...
, via Kripke models
Kripke semantics
Kripke semantics is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems...
. Montague pioneered this approach in the 1960s and early 1970s.
Montague's thesis was that natural language
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
s (like English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
) and formal language
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
s (like programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
s) 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
Noam Chomsky
Avram Noam Chomsky is an American linguist, philosopher, cognitive scientist, and activist. He is an Institute Professor and Professor in the Department of Linguistics & Philosophy at MIT, where he has worked for over 50 years. Chomsky has been described as the "father of modern linguistics" and...
and his associates." (Universal Grammar 1970)
Montague published what soon became known as Montague grammar in three seminal papers:
- 1970: "Universal grammar" (= UG)
- 1970: "English as a Formal Language" (= EFL)
- 1973: "The Proper Treatment of Quantification in Ordinary English" (= PTQ)
Montague's treatment of quantification
Quantification
Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...
has been linked to the notion of continuation
Continuation
In computer science and programming, a continuation is an abstract representation of the control state of a computer program. A continuation reifies the program control state, i.e...
in programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
.
Further reading
- Richmond Thomason (ed.): Formal Philosophy. Selected Papers by Richard Montague. New Haven, 1974, ISBN 0300024126
- Paul Portner, Barbara H. Partee (eds.): Formal SemanticsFormal semantics (linguistics)In linguistics, formal semantics seeks to understand linguistic meaning by constructing precise mathematical models of the principles that speakers use to define relations between expressions in a natural language and the world which supports meaningful discourse.The mathematical tools used are the...
: The Essential Readings, Blackwell, 2002. ISBN 0631215425 - D.R. DowtyDavid DowtyDavid Dowty is a linguist known primarily for his work in semantic and syntactic theory, and especially in Montague grammar and Categorial grammar. Dr. Dowty is a professor emeritus of linguistics at the Ohio State University.-Publications:...
, R.E. Wall and S. Peters: Introduction to Montague Semantics. Kluwer Academic Publishers, 1981, ISBN 9027711429 - Emmon BachEmmon BachEmmon Bach is an American linguist. He is Professor Emeritus at theDepartment of Linguistics, University of Massachusetts, Amherst and Professorial Research Associate at the School of Oriental and African Studies , part of the University of London...
: 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 BenthemJohan van Benthem (logician)Johannes Franciscus Abraham Karel van Benthem is a University Professor of logic at the University of Amsterdam at the Institute for Logic, Language and Computation and professor of philosophy at Stanford University . He was awarded the Spinozapremie in 1996.He studied physics , philosophy...
and A.G.B. ter Meulen ElsevierElsevierElsevier is a publishing company which publishes medical and scientific literature. It is a part of the Reed Elsevier group. Based in Amsterdam, the company has operations in the United Kingdom, USA and elsewhere....
/MIT PressMIT PressThe MIT Press is a university press affiliated with the Massachusetts Institute of Technology in Cambridge, Massachusetts .-History:...
, 1997, pp. 5–92. ISBN 0262220539 - Reinhard Muskens Type-logical Semantics to appear in the Routledge Encyclopedia of Philosophy Online (contains an annotated bibliography).
See also
- Categorial grammarCategorial grammarCategorial grammar is a term used for a family of formalisms in natural language syntax motivated by the principle of compositionality and organized according to the view that syntactic constituents should generally combine as functions or according to a function-argument relationship...
- Continuation-passing styleContinuation-passing styleIn functional programming, continuation-passing style is a style of programming in which control is passed explicitly in the form of a continuation. Gerald Jay Sussman and Guy L. Steele, Jr...
- LojbanLojbanSee also discussed by Arthur Protin, Bob LeChevalier, Carl Burke, Doug Landauer, Guy Steele, Jack Waugh, Jeff Prothero, Jim Carter, and Robert Chassell, as well as , the concepts which "average English speakers won't recognize" because most of them "have no exact English counterpart".Like most...
- Kripke semanticsKripke semanticsKripke semantics is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems...
- Situation semanticsSituation semanticsSituation semantics, pioneered by Jon Barwise and John Perry in the early 1980s, attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, philosophy, or applied natural language...
External links
- A Free Montague Parser in a non-deterministic extension of Common LispCommon LispCommon Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...
. - Montague Grammar in historical context. / The theory and the substance of Montague grammar. Central principles. / Further developments and controversies. by Barbara H. Partee.