Abstract
Every language recognized by the Lambek calculus with brackets is context-free. This is shown by combining an observation by Jäger with an entirely straightforward adaptation of the method Pentus used for the original Lambek calculus. The case of the variant of the calculus allowing sequents with empty antecedents is slightly more complicated, requiring a restricted use of the multiplicative unit.
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DOI 10.1007/s10849-018-9269-3
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References found in this work BETA

The Mathematics of Sentence Structure.Joachim Lambek - 1968 - Journal of Symbolic Logic 33 (4):627-628.
Multimodal Linguistic Inference.Michael Moortgat - 1996 - Journal of Logic, Language and Information 5 (3-4):349-385.
Product-Free Lambek Calculus and Context-Free Grammars.Mati Pentus - 1997 - Journal of Symbolic Logic 62 (2):648-660.
Computing Interpolants in Implicational Logics.Makoto Kanazawa - 2006 - Annals of Pure and Applied Logic 142 (1):125-201.
Product-Free Lambek Calculus and Context-Free Grammars.Mati Pentus - 1997 - Journal of Symbolic Logic 62 (2):648-660.

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