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, and arguably it was already assumed by George Boole 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 contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations.

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. 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.

A common formulation 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."

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. 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.

On a sentence level, the principle claims that what remains if one removes the lexical parts of a meaningful 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 contextuality, the non compositionality of idiomatic expressions, and the non compositionality of quotations.

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.