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abbreviatory variable arithmetically dense AS'A basic rule Brian Cantwell Smith c(m+ CF language class of phenomena class of r.e. closed under intersection constrained context-free language context-sensitive languages derivation A1 derived rule directly yields encode essential variables finite set finitely many metarules Formal Properties Forthcoming Gazdar and Pullum Gerald Gazdar GPSG grammar G grammars without phantom handled by metarules infinite rule sets interaction between metarules Johan van Benthem Jon Barwise Josť Meseguer Joseph Goguen lemma Let G metarule containing metarule of G MPS grammars MPS/1 grammar natural languages nonrecursive languages occur phantom categories phantom symbols Phrase Structure Grammar r.e. languages r.e. relation r.e. set range recursive language recursively enumerable right-hand side rule derivations rule of G satisfies the hypotheses Semantics set of strings Shieber terminal and nonterminal terminal string useless symbol UV'v verb vocabulary VT VP rules Weak Generative Capacity