Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dialectics of Counting and the Mathematics of Vagueness   New concepts of rough natural number systems are introduced in this research
paper from both formal and less formal perspectives. These are used to improve
most rough set-theoretical measures in general Rough Set theory (\textsf{RST})
and to represent rough semantics. The foundations of the theory also rely upon
the axiomatic approach to granularity for all types of general \textsf{RST}
recently developed by the present author. The latter theory is expanded upon in
this paper. It is also shown that algebraic semantics of classical \textsf{RST}
can be obtained from the developed dialectical counting procedures. Fuzzy set
theory is also shown to be representable in purely granule-theoretic terms in
the general perspective of solving the contamination problem that pervades this
research paper. All this constitutes a radically different approach to the
mathematics of vague phenomena and suggests new directions for a more realistic
extension of the foundations of mathematics of vagueness from both foundational
and application points of view. Algebras corresponding to a concept of
\emph{rough naturals} are also studied and variants are characterised in the
penultimate section.

29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ