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Principle of compositionality

 

 
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Principle of compositionality
 
 
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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, semantics
Semantics

Semantics is the study of meaning in communication. The word is derived from the Greek language word s??a?t???? , "significant", from s??a??? , "to signify, to indicate" and that from s??a , "sign, mark, token"....
, and philosophy of language
Philosophy of language

Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for Analytic philosophys is concerned with four central problems: the nature of Meaning , language use, language cognition, and the relationship between language and reality....
, the Principle of Compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This principle is also called Frege's Principle, because Gottlob Frege
Gottlob Frege

Friedrich Ludwig Gottlob Frege was a Germany mathematics who became a logician and philosophy. He helped found both modern mathematical logic and analytic philosophy....
 is widely credited for the first modern formulation of it. However, the idea appears already among India
India

India, officially the Republic of India , is a country in South Asia. It is the List of countries and outlying territories by total area country by geographical area, the List of countries by population country, and the most populous liberal democracy in the world....
n philosophers of grammar such as Yaska
Yaska

, was a Sanskrit grammarian who preceded Panini. His famous text is Nirukta, which deals with etymology, lexical category and the semantics of words....
, and also in Plato
Plato

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
's work such as in Theaetetus
Theaetetus (dialogue)

The The?tetus is one of Plato's Dialogues of Plato concerning the epistemology. The framing of the dialogue begins when Euclid of Megara tells his friend Terpsion that he had written a book many years ago based on what Socrates had told him of a conversation he'd had with Theaetetus when [Theaetetus] was quite a young man....
.

The principle of compositionality states that in a meaningful sentence, if the lexical parts are taken out of the sentence, what remains will be the rules of composition.






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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, semantics
Semantics

Semantics is the study of meaning in communication. The word is derived from the Greek language word s??a?t???? , "significant", from s??a??? , "to signify, to indicate" and that from s??a , "sign, mark, token"....
, and philosophy of language
Philosophy of language

Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for Analytic philosophys is concerned with four central problems: the nature of Meaning , language use, language cognition, and the relationship between language and reality....
, the Principle of Compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This principle is also called Frege's Principle, because Gottlob Frege
Gottlob Frege

Friedrich Ludwig Gottlob Frege was a Germany mathematics who became a logician and philosophy. He helped found both modern mathematical logic and analytic philosophy....
 is widely credited for the first modern formulation of it. However, the idea appears already among India
India

India, officially the Republic of India , is a country in South Asia. It is the List of countries and outlying territories by total area country by geographical area, the List of countries by population country, and the most populous liberal democracy in the world....
n philosophers of grammar such as Yaska
Yaska

, was a Sanskrit grammarian who preceded Panini. His famous text is Nirukta, which deals with etymology, lexical category and the semantics of words....
, and also in Plato
Plato

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
's work such as in Theaetetus
Theaetetus (dialogue)

The The?tetus is one of Plato's Dialogues of Plato concerning the epistemology. The framing of the dialogue begins when Euclid of Megara tells his friend Terpsion that he had written a book many years ago based on what Socrates had told him of a conversation he'd had with Theaetetus when [Theaetetus] was quite a young man....
.

The principle of compositionality states that in a meaningful sentence, if the lexical parts are taken out of the sentence, what remains will be the rules of composition. Take, for example, the sentence "Socrates was a man". Once the meaningful lexical items are taken away - "Socrates" and "man" - what is left is the pseudo-sentence, "S was a M". The task becomes a matter of describing what the connection is between S and M.

It is frequently taken to mean that every operation of the syntax should be associated with an operation of the semantics that acts on the meanings of the constituents combined by the syntactic operation. As a guideline for constructing semantic theories, this is generally taken, as in the influential work on the philosophy of language by Donald Davidson
Donald Davidson (philosopher)

Donald Herbert Davidson was an United States philosopher, who served as Slusser Professor of Philosophy at the University of California, Berkeley, from 1981 to 2003, after having also held substantive teaching appointments at Stanford University, Rockefeller University, Princeton University and the University of Chicago....
, to mean that every construct of the syntax
Syntax

In linguistics, syntax is the study of the principles and rules for constructing Sentence s in natural languages. In addition to referring to the discipline, the term syntax is also used to refer directly to the rules and principles that govern the sentence structure of any individual language, as in "the Irish syntax"....
 should be associated by a clause of the T-schema
T-schema

The T-schema or truth schema is the inductive definition that lies at the heart of any realisation of Alfred Tarski's semantic theory of truth, expressing the commutation of truth over logical operators....
 with an operator in the semantics
Semantics

Semantics is the study of meaning in communication. The word is derived from the Greek language word s??a?t???? , "significant", from s??a??? , "to signify, to indicate" and that from s??a , "sign, mark, token"....
 that specifies how the meaning of the whole expression is built from constituents combined by the syntactic rule. In some general mathematical theories (especially those in the tradition of Montague grammar
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 lambda calculus and set theory, and makes use of the notions of intensional logic and type theory....
) this guideline is taken to mean that the interpretation of a language is essentially given by a homomorphism
Homomorphism

In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ???? meaning "same" and ???f? meaning "shape"....
 between an algebra of syntactic representations and an algebra of semantic objects.

The Principle of Compositionality also exists in a similar form in the compositionality of programming languages
Denotational semantics of the Actor model

The denotational semantics of the Actor model is the subject of denotational domain theory for Actor model. The historical development of this subject is recounted in [Hewitt 2008b]....
.

Critiques


The principle of compositionality has been the subject of intense debate. Indeed, there is no general agreement as to how the principle is to be interpreted, although there have been several attempts to provide formal definitions of it.

Scholars are also divided as to whether the principle should be regarded as a factual claim, open to empirical
Empirical

The word empirical denotes information gained by means of observation, experience, or experiment, as opposed to theory. A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or Logical consequence that are observable by the senses....
 testing; an analytic
Analytic

Generally speaking, analytic refers to the "having the ability to analyze" or "division into elements or principles."It can also have the following meanings:...
 truth, obvious from the nature of language and meaning; or a methodological
Methodology

Methodology can be defined as:# "the analysis of the principles of methods, rules, and postulates employed by a discipline";# "the systematic study of methods that are, can be, or have been applied within a discipline"; or...
 principle to guide the development of theories of syntax and semantics. The principle has been attacked in all three spheres, although so far none of the criticisms brought against it have been generally regarded as compelling. Most proponents of the principle, however, make certain exceptions for idiomatic expressions in natural language.

Further, in the context of the philosophy of language, the principle of compositionality does not explain all of meaning. For example, you cannot infer sarcasm
Sarcasm

Sarcasm is a form of ironic speech or writing which is bitter or cutting, being intended to taunt its target. It is first recorded in English in The Shepheardes Calender in 1579: ...
 purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly. The principle of compositionality, then, has to be revised to take into account linguistic and extralinguistic context
Context principle

In the philosophy of language, the context principle is a form of semantic holism holding that a philosopher should "never ... ask for the meaning of a word in isolation, but only in the context of a proposition" ....
, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.

See also

  • Referential transparency (computer science)
  • Initial algebra
    Initial algebra

    In mathematics, an initial algebra is an initial object in the F-algebra for a given endofunctor F. The initiality provides a general framework for mathematical induction and recursion....
  • Componential analysis
    Componential analysis

    Componential analysis, also called feature analysis or contrast analysis, refers to the description of the meaning of words through structured sets of semantics features, which are given as ?present?, ?absent? or ?indifferent with reference to feature?....


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