Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Constructive Logic with Classical Proofs and Refutations (Extended
  Version)   We study a conservative extension of classical propositional logic
distinguishing between four modes of statement: a proposition may be affirmed
or denied, and it may be strong or classical. Proofs of strong propositions
must be constructive in some sense, whereas proofs of classical propositions
proceed by contradiction. The system, in natural deduction style, is shown to
be sound and complete with respect to a Kripke semantics. We develop the system
from the perspective of the propositions-as-types correspondence by deriving a
term assignment system with confluent reduction. The proof of strong
normalization relies on a translation to System F with Mendler-style recursion.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th