Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bunch theory: working notes on applications, axioms and models   In his book A Practical Theory of Programming, Eric Hehner proposes and
applies a remarkably radical reformulation of set theory, in which the
collection and packaging of elements are seen as separate activities. This
provides for unpackaged collections, referred to as bunches. Bunches allow us
to reason about non-determinism at the level of terms, and, very remarkably,
allow us to reason about the conceptual entity nothing, which is just an empty
bunch (and very different from an empty set). This eliminates mathematical gaps
caused by undefined terms. We compare the use of bunches with other approaches
to this problem, and we illustrate the use of Bunch Theory in formulating
program semantics combining non-deterministic, preferential, and probabilistic
choice to provide a guarded command language whose exceptional expressivity we
illustrate with a short case study. We show how an existing axiomatisation of
set theory can be extended to incorporate bunches, and we provide and validate
a model.

14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg