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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. This principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the idea appears already among Indian philosophers of grammar such as Y?ska, and also in Plato's work such as in Theaetetus. Besides, the principle was never explicitly stated by Frege, and it was arguably already assumed by Boole decades before Frege’s work.
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 ass . . . more
https://en.wikipedia.org/wiki/Principle_of_compositionality
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