Abstract

We demonstrate that for all practical purposes, Lambek Grammars (LG) are strongly equivalent to Context-Free Grammars (CFG) and hence to second-order Abstract Categorial Grammars (ACG). To be precise, for any Lambek Grammar LG there exists a second-order ACG with a second-order lexicon such that: the set of LG derivations (with a bound on the ‘nesting’ of introduction rules) is the abstract language of the ACG, and the set of yields of those derivations is its object language. Furthermore, the LG lexicon is represented in the abstract ACG signature with no duplications. The fixed, and small, bound on the nesting of introduction rules seems adequate for natural languages. One may therefore say that ACGs are not merely just as expressive as LG, but strongly equivalent.

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