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Gaifman's theorem on categorial grammars revisited

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Abstract

The equivalence of (classical) categorial grammars and context-free grammars, proved by Gaifman [4], is a very basic result of the theory of formal grammars (an essentially equivalent result is known as the Greibach normal form theorem [1], [14]). We analyse the contents of Gaifman's theorem within the framework of structure and type transformations. We give a new proof of this theorem which relies on the algebra of phrase structures and exhibit a possibility to justify the key construction used in Gaifman's proof by means of the Lambek calculus of syntactic types [15].

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Buszkowski, W. Gaifman's theorem on categorial grammars revisited. Stud Logica 47, 23–33 (1988). https://doi.org/10.1007/BF00374049

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