Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decision Problems for Propositional Non-associative Linear Logic and
  Extensions   In our previous work, we proposed the logic obtained from full
non-associative Lambek calculus by adding a sort of linear-logical modality. We
call this logic non-associative non-commutative intuitionistic linear logic
($\mathbf{NACILL}$, for short). In this paper, we establish the decidability
and undecidability results for various extensions of $\mathbf{NACILL}$.
Regarding the decidability results, we show that the deducibility problems for
several extensions of $\mathbf{NACILL}$ with the rule of left-weakening are
decidable. Regarding the undecidability results, we show that the provability
problems for all the extensions of non-associative non-commutative classical
linear logic by the rules of contraction and exchange are undecidable.

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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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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: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph