Eliminating the unit constant in the Lambek calculus with brackets
نویسنده
چکیده
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).
منابع مشابه
On the Recognizing Power of the Lambek Calculus with Brackets
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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عنوان ژورنال:
- CoRR
دوره abs/1711.06361 شماره
صفحات -
تاریخ انتشار 2017