Editing Principle of compositionality (section)

==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}}</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]].