Compositional Semantics for Linguistic Formalisms Shuly Wintner In what sense is a grammar the union of its rules? This paper adapts the notion of \textit{composition}, well developed in the context of programming languages, to the domain of linguistic formalisms. We study alternative definitions for the semantics of such formalisms, suggesting a denotational semantics that we show to be compositional and fully-abstract. This facilitates a clear, mathematically sound way for defining grammar modularity.