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تسجيل مستخدم جديدEliminating the unit constant in the Lambek calculus with brackets
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Stepan Kuznetsov
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We present a translation of the Lambek calculus with brackets and the unit constant, $mathbf{Lb}^{boldsymbol{*}}_{mathbf{1}}$, into the Lambek calculus with brackets allowing empty antecedents, but without the unit constant, $mathbf{Lb}^{boldsymbol{*}}$. Using this translation, we extend previously known results for $mathbf{Lb}^{boldsymbol{*}}$ to $mathbf{Lb}^{boldsymbol{*}}_{mathbf{1}}$: (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).
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