Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dialectica Categories for the Lambek Calculus   We revisit the old work of de Paiva on the models of the Lambek Calculus in
dialectica models making sure that the syntactic details that were sketchy on
the first version got completed and verified. We extend the Lambek Calculus
with a \kappa modality, inspired by Yetter's work, which makes the calculus
commutative. Then we add the of-course modality !, as Girard did, to
re-introduce weakening and contraction for all formulas and get back the full
power of intuitionistic and classical logic. We also present the categorical
semantics, proved sound and complete. Finally we show the traditional
properties of type systems, like subject reduction, the Church-Rosser theorem
and normalization for the calculi of extended modalities, which we did not have
before.

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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
9
The categories of this paper are: nlin
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The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat