Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical linear logic, cobordisms and categorial grammars   We propose a categorial grammar based on classical multiplicative linear
logic.
  This can be seen as an extension of abstract categorial grammars (ACG) and is
at least as expressive. However, constituents of {\it linear logic grammars
(LLG)} are not abstract ${\lambda}$-terms, but simply tuples of words with
labeled endpoints and supplied with specific {\it plugging instructions}: the
sets of endpoints are subdivided into the {\it incoming} and the {\it outgoing}
parts. We call such objects {\it word cobordisms}.
  A key observation is that word cobordisms can be organized in a category,
very similar to the familiar category of topological cobordisms. This category
is symmetric monoidal closed and compact closed and thus is a model of linear
$\lambda$-calculus and classical, as well as intuitionistic linear logic. This
allows us using linear logic as a typing system for word cobordisms.
  At least, this gives a concrete and intuitive representation of ACG.
  We think, however, that the category of word cobordisms, which has a rich
structure and is independent of any grammar, might be interesting on its own
right.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th