Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cut elimination, identity elimination, and interpolation in super-Belnap
  logics   We develop a Gentzen-style proof theory for super-Belnap logics (extensions
of the four-valued Dunn-Belnap logic), expanding on an approach initiated by
Pynko. We show that just like substructural logics may be understood
proof-theoretically as logics which relax the structural rules of classical
logic but keep its logical rules as well as the rules of Identity and Cut,
super-Belnap logics may be seen as logics which relax Identity and Cut but keep
the logical rules as well as the structural rules of classical logic. A
generalization of the cut elimination theorem for classical propositional logic
is then proved and used to establish interpolation for various super-Belnap
logics. In particular, we obtain an alternative syntactic proof of a refinement
of the Craig interpolation theorem for classical propositional logic discovered
recently by Milne.

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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg