Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: De Morgan Dual Nominal Quantifiers Modelling Private Names in
  Non-Commutative Logic   This paper explores the proof theory necessary for recommending an expressive
but decidable first-order system, named MAV1, featuring a de Morgan dual pair
of nominal quantifiers. These nominal quantifiers called `new' and `wen' are
distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifiers.
The novelty of these nominal quantifiers is they are polarised in the sense
that `new' distributes over positive operators while `wen' distributes over
negative operators. This greater control of bookkeeping enables private names
to be modelled in processes embedded as formulae in MAV1. The technical
challenge is to establish a cut elimination result, from which essential
properties including the transitivity of implication follow. Since the system
is defined using the calculus of structures, a generalisation of the sequent
calculus, novel techniques are employed. The proof relies on an intricately
designed multiset-based measure of the size of a proof, which is used to guide
a normalisation technique called splitting. The presence of equivariance, which
swaps successive quantifiers, induces complex inter-dependencies between
nominal quantifiers, additive conjunction and multiplicative operators in the
proof of splitting. Every rule is justified by an example demonstrating why the
rule is necessary for soundly embedding processes and ensuring that cut
elimination holds.

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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph