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{{Short description|Principle in linguistics about meaning}}
{{Linguistics}}{{Semantics}}
In [[semantics]], [[mathematical logic]] 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. The principle is also called '''Frege's principle''', because [[Gottlob Frege]] is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege,<ref>{{Cite journal |last=Pelletier |first=Francis Jeffry |date=2001 |title=Did Frege Believe Frege's Principle? |url=http://link.springer.com/10.1023/A:1026594023292 |journal=Journal of Logic, Language and Information |volume=10 |issue=1 |pages=87–114 |doi=10.1023/A:1026594023292|url-access=subscription }}</ref> and arguably it was already assumed by [[George Boole]]<ref>Boole, G. (1854). ''An investigation of the laws of thought: on which are founded the mathematical theories of logic and probabilities''. Walton and Maberly.</ref> decades before Frege's work.

The principle of compositionality (also known as '''semantic compositionalism''') is highly debated in linguistics. Among its most challenging problems there are the issues of [[Context (language use)|contextuality]], the non-compositionality of [[idiomatic expression]]s, and the non-compositionality of [[quotation]]s.<ref name="Pelletier2016sec12"/>

== 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 [[context (language use)|contextuality]], and compositionality was usually preferred.<ref name=":0">{{Cite journal |last=Janssen |first=Theo |date=2012 |title=Compositionality: Its Historic Context |url=https://academic.oup.com/edited-volume/41264/chapter/350861043 |journal=Oxford Handbook of Compositionality |pages=19–46 |doi=10.1093/oxfordhb/9780199541072.013.0001|url-access=subscription }}</ref> [[Gottlob Frege]] never adhered to the principle of compositionality as it is known today (Frege endorsed the [[context principle]] instead), and the first to explicitly formulate it was [[Rudolf Carnap]] in 1947.<ref name=":0" />

==Overview==
A common formulation<ref name=":0" /> of the principle of compositionality comes from [[Barbara Partee]], stating: "The meaning of a compound expression is a function of the meanings of its parts and of the way they are syntactically combined."<ref>{{Cite journal |last=Partee |first=Barbara |date=1984 |title=Compositionality |journal=Varieties of Formal Semantics |volume=3 |pages=281–311}}</ref>

It is possible to distinguish different levels of compositionality. Strong compositionality refers to compound expressions that are determined by the meaning of its ''immediate'' parts and a top-level syntactic function that describes their combination. Weak compositionality refers to compound expressions that are determined by the meaning of its parts as well as their complete syntactic combination.<ref>{{Cite journal |last1=Coopmans |first1=Cas W. |last2=Kaushik |first2=Karthikeya |last3=Martin |first3=Andrea E. |date=2023 |title=Hierarchical structure in language and action: A formal comparison. |url=http://doi.apa.org/getdoi.cfm?doi=10.1037/rev0000429 |journal=Psychological Review |language=en |volume=130 |issue=4 |pages=935–952 |doi=10.1037/rev0000429 |pmid=37166848 |issn=1939-1471|url-access=subscription }}</ref><ref name=":1">{{Cite journal |last1=Pagin |first1=Peter |last2=Westerståhl |first2=Dag |date=2010 |title=Compositionality I: Definitions and Variants |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1747-9991.2009.00228.x |journal=Philosophy Compass |language=en |volume=5 |issue=3 |pages=250–264 |doi=10.1111/j.1747-9991.2009.00228.x|url-access=subscription }}</ref> However, there can also be further gradations in between these two extremes. This is possible, if one not only allows the meaning of immediate parts but also the meaning of the second-highest parts (third-highest parts, fourth-highest parts, etc.) together with functions that describes their respective combinations.<ref name=":1" />

On a sentence level, the principle claims that what remains if one removes the [[lexical (semiotics)|lexical]] parts of a meaningful [[Sentence (linguistics)|sentence]], are the rules of composition. The sentence "Socrates was a man", for example, becomes "S was a M"  once the meaningful lexical items—"Socrates" and "man"—are taken away. The task of finding the rules of composition, then becomes a matter of describing what the connection between S and M is.

Among the most prominent linguistic problems that challenge the principle of compositionality are the issues of [[Context (language use)|contextuality]], the non compositionality of [[idiomatic expression]]s, and the non compositionality of [[quotation]]s.<ref name="Pelletier2016sec12">Pelletier (2016) section ''"12 This Chapter"''</ref>

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 (philosopher)|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]]), this guideline is taken to mean that the interpretation of a language is essentially given by a [[homomorphism]] between an algebra of syntactic representations and an algebra of semantic objects.

The principle of compositionality also exists in a similar form in the [[Denotational semantics#Compositionality|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.<ref name="Szabó2012">Szabó, Zoltán Gendler (2012) "[https://web.archive.org/web/20130117194209/https://plato.stanford.edu/entries/compositionality/ Compositionality]". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. First published Thu Apr 8, 2004; substantive revision Fri Dec 7, 2012</ref>

Scholars are also divided as to whether the principle should be regarded as a factual claim, open to [[empirical]] testing; an [[Logical truth|analytic truth]], obvious from the nature of language and meaning; or a [[methodology|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.{{citation needed|date=June 2021}} Most proponents of the principle, however, make certain exceptions for [[idiomatic]] expressions in natural language.<ref name="Szabó2012"/>

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 (language use)|context]], [[semantic memory]], or [[sensory cue]]s.<ref>Baggio et al. (2012), Conclusions.</ref> Among the problematic phenomena for traditional theories of compositionality is that of [[logical metonymy]], which has been studied at least since the mid 1990s by linguists [[James Pustejovsky]] and [[Ray Jackendoff]].<ref name="Chersoni2017">Chersoni, E., Lenci, A., & Blache, P. (2017, August). ''[https://hal.archives-ouvertes.fr/hal-01572187/ Logical metonymy in a distributional model of sentence comprehension]''. In Sixth Joint Conference on Lexical and Computational Semantics (* SEM 2017) (pp. 168-177).</ref><ref>James Pustejovsky. 1995. The Generative Lexicon. The MIT Press, Cambridge, MA</ref><ref>Ray Jackendoff. 1997. The Architecture of the Language Faculty. The MIT Press, Cambridge, MA.</ref> Logical metonymies are sentences like ''John began the book'', where the verb ''to begin'' requires ([[subcategorization|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).<ref name="Chersoni2017"/> 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 principle|context]], which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.<ref name="Szabó2012"/>

==See also==
*[[Componential analysis]]
*[[Context principle]]
*[[Semantics (computer science)]]
*[[Semantics of logic]]
*[[Garden-path sentence]]
*[[Initial algebra]]
*[[Levels of Processing model]]
*[[Opaque context]] &mdash; another problem for compositionality
*[[Referential transparency]] &mdash; in programming languages
*[[Semantic decomposition (natural language processing)]]

==Notes==
{{reflist}}

==References==
* Baggio, G., Van Lambalgen, M., & Hagoort, P. (2012) ''[https://pure.mpg.de/rest/items/item_66821_17/component/file_933167/content The processing consequences of compositionality]'', in M. Werning, W. Hinzen, & E. Machery (Eds.), ''[https://books.google.com/books?id=-UYfAQAAQBAJ&pg=PA655 The Oxford handbook of compositionality]'' (pp.&nbsp;655–672). 
* Janssen, T. M. (2012) ''[https://pure.uva.nl/ws/files/1159272/105371_HandbookJanssen.pdf Compositionality: Its historic context]'', in M. Werning, W. Hinzen, & E. Machery (Eds.), ''[https://books.google.com/books?id=-UYfAQAAQBAJ&pg=PA655 The Oxford handbook of compositionality]'', pp.&nbsp;19–46, Oxford University Press.
* Pelletier, Francis Jeffry (2001) ''[http://www.sfu.ca/~jeffpell/papers/FregesPrinciplePublished.pdf Did Frege believe Frege’s principle?]'', in ''Journal of Logic, Language and Information'' 10:87–114.
* Pelletier, Francis Jeffry (2016) ''[https://oxfordre.com/linguistics/view/10.1093/acrefore/9780199384655.001.0001/acrefore-9780199384655-e-42?rskey=tdaoHr&result=54 Semantic Compositionality]'' in [[Mark Aronoff|M. Aronoff]] (ed) ''[https://oxfordre.com/linguistics/ The Oxford Research Encyclopedia of Linguistics]'', Oxford UP.

==Further reading==
* Ferreira, F., Bailey, K. G., & Ferraro, V. (2002). ''[http://www2.psychology.uiowa.edu/faculty/hollingworth/prosem/Ferreira-2002-Good-enough%20represen.pdf Good-enough representations in language comprehension]'' in ''Current directions in psychological science'', 11(1), 11-15.
* Ferreira, F., & Patson, N. D. (2007). ''[http://www.lib.csu.ru/ER/ER_Philosophy/fulltexts/FerreiraF.pdf The ‘good enough’approach to language comprehension]'' in ''Language and Linguistics Compass'', 1(1‐2), 71-83.
*{{cite SEP |url-id=compositionality |title=Compositionality |last=Szabó |first=Zoltán Gendler}} (2004) revisions in [https://web.archive.org/web/20060914153422/https://plato.stanford.edu/entries/compositionality/ 2005], [https://web.archive.org/web/20070609104112/http://plato.stanford.edu/entries/compositionality/ 2007], [https://web.archive.org/web/20130117194209/https://plato.stanford.edu/entries/compositionality/ 2012], [https://web.archive.org/web/20171211045030/https://plato.stanford.edu/entries/compositionality/ 2017], [https://web.archive.org/web/20201101133238/https://plato.stanford.edu/entries/compositionality/ 2020].
* Werning, Markus; & Edouard Machery, & Gerhard Schurz (Eds., 2004) ''[http://ontosverlag.de/index.php?page=shop.product_details&flypage=flypage.tpl&product_id=86&category_id=10&option=com_virtuemart&Itemid=1 The Compositionality of Meaning and Content]'', Vol. I & II, Ontos 
* Werning, Markus; & Wolfram Hinzen, & Edouard Machery (Eds., 2012) ''[http://ukcatalogue.oup.com/product/9780199541072.do The Oxford Handbook of Compositionality]'', Oxford University Press

{{philosophy of language}}
{{Formal semantics}}

[[Category:Semantics]]
[[Category:Principles]]
[[Category:Philosophy of language]]
[[Category:Syntax–semantics interface]]
[[Category:Formal semantics (natural language)]]