Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eliminating the unit constant in the Lambek calculus with brackets   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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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: eess