The design, implementation, and use of grammar formalisms for natural language have constituted a major branch of computational linguistics throughout its development. By viewing gramn, ar formalisms as just a special cause of computer languages, we can take advantage of the machinery of dcnoational semantics to provide a pre- cise 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 PATRI1, and provide a dcnotational semantics for a simple gram- mar 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.