Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Undecidability of the Lambek calculus with a relevant modality   Morrill and Valentin in the paper "Computational coverage of TLG:
Nonlinearity" considered an extension of the Lambek calculus enriched by a
so-called "exponential" modality. This modality behaves in the "relevant"
style, that is, it allows contraction and permutation, but not weakening.
Morrill and Valentin stated an open problem whether this system is decidable.
Here we show its undecidability. Our result remains valid if we consider the
fragment where all division operations have one direction. We also show that
the derivability problem in a restricted case, where the modality can be
applied only to variables (primitive types), is decidable and belongs to the NP
class.

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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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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: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an