 Compositional semantics

Compositional semantics explains a complex expression's meaning through the meanings of its parts and the way syntax combines them. It requires a rule of combination, not merely a list of word meanings. This helps explain how a speaker can understand unfamiliar combinations of familiar material.^[ref]

In an original toy model, let the red objects be $R=\{1,2\}$ and round objects $O=\{2,3\}$. Treating red and round as an intersection gives $R\cap O=\{2\}$. Replacing and with or calls for a different combination, giving $R\cup O=\{1,2,3\}$. This stipulated analysis makes the connective's contribution explicit. Natural expressions require more care: not every adjective combines with a noun by intersection. A proposed formal semantics must specify its rules and check their predictions against interpretations.