Abstract
An essential prerequisite for modular grammar design is a clear, mathematically well-founded definition for the semantics of grammar formalisms, facilitating reasoning about grammars and their computational properties. This paper shows that existing definitions for the semantics of unification grammars, both operational and denotational, are not compositional with respect to a simple and natural grammar combination operator. Adapting results from the semantics of logic programming languages, we suggest a denotational semantics that we show to be both compositional and fully-abstract. This semantics induces an equivalence relation by which two grammars are equivalent if and only if they can be interchanged in any context. This provides a clear, mathematically sound way for defining grammar modularity.
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