Eliminating the unit constant in the Lambek calculus with brackets

11/17/2017

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by   Stepan Kuznetsov, et al.

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We present a translation of the Lambek calculus with brackets and the unit constant, Lb^*_1, into the Lambek calculus with brackets allowing empty antecedents, but without the unit constant, Lb^*. Using this translation, we extend previously known results for Lb^* to Lb^*_1: (1) languages generated by categorial grammars based on the Lambek calculus with brackets are context-free (Kanazawa 2017); (2) the polynomial-time algorithm for deciding derivability of bounded depth sequents (Kanovich et al. 2017).