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In mathematics, semantics, and philosophy of language, 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 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, 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.

This principle is sometimes called Frege's Principle, because Frege is widely credited for the first formulation of it. This claim has also been disputed.

The Principle of Compositionality also exists in a similar form in the compositionality of programming languages.

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 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 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 purely on the basis of words and their composition, yet a phrase used sarcastically means something completely different from the same phrase uttered seriously. The principle of compositionality, then, has to be revised to take into account linguistic and extralinguistic context, which includes the tone of voice used, common ground between the speakers, the intentions of the speaker, and so on.

• Referential transparency
• Initial algebra
• Componential analysis

• Stanford Encyclopedia of Philosophy entry
• Anthologies on compositionality
• Overview