Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Worm Calculus   We present a propositional modal logic $\sf WC$, which includes a logical
$verum$ constant $\top$ but does not have any propositional variables.
Furthermore, the only connectives in the language of $\sf WC$ are
consistency-operators $\langle \alpha \rangle$ for each ordinal $\alpha$. As
such, we end up with a class-size logic. However, for all practical purposes,
we can consider restrictions of $\sf WC$ up to a given ordinal. Given the
restrictive signature of the language, the only formulas are iterated
consistency statements, which are called worms. The theorems of $\sf WC$ are
all of the form $A \vdash B$ for worms $A$ and $B$.
  The main result of the paper says that the well-known strictly positive logic
$\sf RC$, called Reflection Calculus, is a conservative extension of $\sf WC$.
As such, our result is important since it is the ultimate step in stripping
spurious complexity off the polymodal provability logic $\sf{GLP}$, as far as
applications to ordinal analyses are concerned. Indeed, it may come as a
surprise that a logic as weak as $\sf WC$ serves the purpose of computing
something as technically involved as the proof theoretical ordinals of formal
mathematical theories.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph