Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Introduction to a Hypergraph Logic Unifying Different Variants of the
  Lambek Calculus   In this paper hypergraph Lambek calculus ($\mathrm{HL}$) is presented. This
formalism aims to generalize the Lambek calculus ($\mathrm{L}$) to hypergraphs
as hyperedge replacement grammars extend context-free grammars. In contrast to
the Lambek calculus, $\mathrm{HL}$ deals with hypergraph types and sequents;
its axioms and rules naturally generalize those of $\mathrm{L}$. Consequently,
certain properties (e.g. the cut elimination) can be lifted from $\mathrm{L}$
to $\mathrm{HL}$. It is shown that $\mathrm{L}$ can be naturally embedded in
$\mathrm{HL}$; moreover, a number of its variants ($\mathrm{LP}$,
$\mathrm{NL}$, $\mathrm{NLP}$, $\mathrm{L}$ with modalities,
$\mathrm{L}^\ast(\mathbf{1})$, $\mathrm{L}^{\mathrm{R}}$) can also be embedded
in $\mathrm{HL}$ via different graph constructions. We also establish a
connection between $\mathrm{HL}$ and Datalog with embedded implications. It is
proved that the parsing problem for $\mathrm{HL}$ is NP-complete.

35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph