The design, implementation, and use of grammar formalisms for natural language have constituted a major branch of computational linguistics throughout its development. By viewing grammar formalisms as just a special case of computer languages, we can take advantage of the machinery of denotational semantics to provide a precise specification of their meaning. Using Dana Scott's domain theory, we elucidate the nature of the feature systems used in augmented phrase-structure grammar formalisms, in particular those of recent versions of generalized phrase structure grammar, lexical functional grammar and PATR-II, and provide a denotational semantics for a simple grammar formalism. We find that the mathematical structures developed for this purpose contain an operation of feature generalization, not available in those grammar formalisms, that can be used to give a partial account of the effect of coordination on syntactic features.
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