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, linguistics and comput ...

mathematical logic Mathematical logic is the study of 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 forma ...

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 p ...

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 George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in ...

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 expression An idiom is a phrase or expression that typically presents a figurative, non-literal meaning attached to the phrase; but some phrases become figurative idioms while retaining the literal meaning of the phrase. Categorized as formulaic language, ...

s, 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 ...

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. ...

in 1947.Janssen (2012)

Overview

The principle of compositionality states that in a meaningful expression, 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. Among the most prominent linguistic problems that challenge the principle of compositionality are the issues of contextuality, the non compositionality of

s, and the non compositionality of

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 ( constituenc ...

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 The T-schema ("truth schema", not to be confused with " Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it ...

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 ...

), this guideline is taken to mean that the interpretation of a language is essentially given by a

homomorphism In algebra, a homomorphism is a morphism, structure-preserving map (mathematics), map between two algebraic structures of the same type (such as two group (mathematics), groups, two ring (mathematics), rings, or two vector spaces). The word ''homo ...

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, 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 Idiom, also called idiomaticness or idiomaticity, is the syntactical, grammatical, or structural form peculiar to a language. Idiom is the realized structure of a language, as opposed to possible but unrealized structures that could have develop ...

expressions in natural language. The principle of compositionality usually holds when only syntactic factors play in the increased complexity of sentence processing, 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 s ...

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 abou ...

, 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 o ...

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 s ...

.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 Sarcasm is the caustic use of words, often in a humorous way, to mock someone or something. Sarcasm may employ ambivalence, although it is not necessarily ironic. Most noticeable in spoken word, sarcasm is mainly distinguished by the inflection ...

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

, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.

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.

History

Overview

Critiques

See also

Notes

References

Further reading