In
semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy
Philosophy (f ...
,
mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
and related disciplines, 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
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic phil ...
is widely credited for the first modern formulation of it. The principle was never explicitly stated by Frege, and it was arguably already assumed by
George Boole decades before Frege's work.
The principle of compositionality is highly debated in linguistics, and among its most challenging problems there are the issues of
contextuality, the non-compositionality of
idiomatic expressions, and the non-compositionality of
quotation
A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written. In oral speech, it is the representation of an utterance (i.e. of something that a speaker actually said) that is introduced by ...
s.
History
Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionality or
contextuality, and compositionality was usually preferred.
Frege (1848-1925) never adhered to the principle of compositionality as it is known today, and the first to explicitly formulate it was Freges' student
Rudolf Carnap
Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. He ...
in 1947.
[Janssen (2012)]
Overview
The principle of compositionality states that in a meaningful expression, if the
lexical
Lexical may refer to:
Linguistics
* Lexical corpus or lexis, a complete set of all words in a language
* Lexical item, a basic unit of lexicographical classification
* Lexicon, the vocabulary of a person, language, or branch of knowledge
* 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.
Among the most prominent linguistic problems that challenge the principle of compositionality are the issues of
contextuality, the non compositionality of
idiomatic expressions, and the non compositionality of
quotation
A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written. In oral speech, it is the representation of an utterance (i.e. of something that a speaker actually said) that is introduced by ...
s.
[Pelletier (2016) section ''"12 This Chapter"'']
It is frequently taken to mean that every operation of the
syntax
In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituency) ...
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, to mean that every construct of the syntax should be associated by a clause of the
T-schema with an operator in the semantics 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 __notoc__
Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use ...
), this guideline is taken to mean that the interpretation of a language is essentially given by a
homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" ...
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.
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.
[Szabó, Zoltán Gendler (2012)]
Compositionality
. In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. First published Thu Apr 8, 2004; substantive revision Fri Dec 7, 2012
Scholars are also divided as to whether the principle should be regarded as a factual claim, open to
empirical
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
testing; an
analytic truth
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...
, obvious from the nature of language and meaning; or a
methodological principle to guide the development of theories of syntax and semantics. The Principle of Compositionality 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.
The principle of compositionality usually holds when only syntactic factors play in the increased complexity of
sentence processing
Sentence processing takes place whenever a reader or listener processes a language utterance, either in isolation or in the context of a conversation or a text. Many studies of the human language comprehension process have focused on reading of s ...
, while it becomes more problematic and questionable when the complexity increase is due to sentence or discourse
context
Context may refer to:
* Context (language use), the relevant constraints of the communicative situation that influence language use, language variation, and discourse summary
Computing
* Context (computing), the virtual environment required to su ...
,
semantic memory
Semantic memory refers to general world knowledge that humans have accumulated throughout their lives. This general knowledge (word meanings, concepts, facts, and ideas) is intertwined in experience and dependent on culture. We can learn about n ...
, or
sensory cue
Sensory may refer to:
Biology
* Sensory ecology, how organisms obtain information about their environment
* Sensory neuron, nerve cell responsible for transmitting information about external stimuli
* Sensory perception, the process of acquiri ...
s. Among the problematic phenomena for traditional theories of compositionality is that of
logical metonymy
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
, which has been studied at least since the mid 1990s by linguists
James Pustejovsky
James Pustejovsky (born 1956) is an American computer scientist. He is the TJX Feldberg professor of computer science at Brandeis University in Waltham, Massachusetts, United States. His expertise includes theoretical and computational modeling of ...
and
Ray Jackendoff
Ray Jackendoff (born January 23, 1945) is an American linguist. He is professor of philosophy, Seth Merrin Chair in the Humanities and, with Daniel Dennett, co-director of the Center for Cognitive Studies at Tufts University. He has always str ...
.
[Chersoni, E., Lenci, A., & Blache, P. (2017, August). ]
Logical metonymy in a distributional model of sentence comprehension
'. In Sixth Joint Conference on Lexical and Computational Semantics (* SEM 2017) (pp. 168-177).[Ray Jackendoff. 1997. The Architecture of the Language Faculty. The MIT Press, Cambridge, MA.] Logical metonymies are sentences like ''John began the book'', where the verb ''to begin'' requires (
subcategorizes) an event as its argument, but in a logical metonymy an object (i.e. ''the book'') is found instead, and this forces to interpret the sentence by inferring an implicit event ("reading", "writing", or other prototypical actions performed on a book).
The problem for compositionality is that the meaning of reading or writing is not present in the words of the sentence, neither in "begin" nor in "book".
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 purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered straightforwardly. Thus, some theorists argue that the principle has to be revised to take into account linguistic and extralinguistic
context
Context may refer to:
* Context (language use), the relevant constraints of the communicative situation that influence language use, language variation, and discourse summary
Computing
* Context (computing), the virtual environment required to su ...
, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.
See also
*
Componential analysis
*
Context principle
*
Semantics (computer science)
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax.
Semantics describes the processes a ...
*
Semantics of logic
In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment.
Overview
The truth con ...
*
Garden-path sentence
*
Initial algebra
*
Levels of Processing model The Levels of Processing model, created by Fergus I. M. Craik and Robert S. Lockhart in 1972, describes memory recall of stimuli as a function of the depth of mental processing. Deeper levels of analysis produce more elaborate, longer-lasting, and ...
*
Opaque context — another problem for compositionality
*
Referential transparency
In computer science, referential transparency and referential opacity are properties of parts of computer programs. An expression is called ''referentially transparent'' if it can be replaced with its corresponding value (and vice-versa) withou ...
— in programming languages
*
Semantic decomposition (natural language processing)
A semantic decomposition is an algorithm that breaks down the meanings of phrases or concepts into less complex concepts. The result of a semantic decomposition is a representation of meaning. This representation can be used for tasks, such as thos ...
Notes
References
* Baggio, G., Van Lambalgen, M., & Hagoort, P. (2012)
The processing consequences of compositionality', in M. Werning, W. Hinzen, & E. Machery (Eds.),
The Oxford handbook of compositionality' (pp. 655–672).
* Janssen, T. M. (2012)
Compositionality: Its historic context', in M. Werning, W. Hinzen, & E. Machery (Eds.),
The Oxford handbook of compositionality', pp. 19-46, Oxford University Press.
* Pelletier, Francis Jeffry (2001)
Did Frege believe Frege’s principle?', in ''Journal of Logic, Language, and Information'' 10:87–114.
* Pelletier, Francis Jeffry (2016)
Semantic Compositionality' in
M. Aronoff (ed)
The Oxford Research Encyclopedia of Linguistics', Oxford UP.
Further reading
* Ferreira, F., Bailey, K. G., & Ferraro, V. (2002).
Good-enough representations in language comprehension' in ''Current directions in psychological science'', 11(1), 11-15.
* Ferreira, F., & Patson, N. D. (2007).
The ‘good enough’approach to language comprehension' in ''Language and Linguistics Compass'', 1(1‐2), 71-83.
* (2004) revisions i
20052007201220172020
* Werning, Markus; & Edouard Machery, & Gerhard Schurz (Eds., 2004)
The Compositionality of Meaning and Content', Vol. I & II, Ontos
* Werning, Markus; & Wolfram Hinzen, & Edouard Machery (Eds., 2012)
The Oxford Handbook of Compositionality', Oxford University Press
{{Formal semantics
Semantics
Principles
Philosophy of language
Formal semantics (natural language)