Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Logic, the $\pi$-calculus, and their Metatheory: A Recipe for
  Proofs as Processes   Initiated by Abramsky [1994], the Proofs as Processes agenda is to establish
a solid foundation for the study of concurrent languages, by researching the
connection between linear logic and the $\pi$-calculus.
  To date, Proofs as Processes is still a partial success. Caires and Pfenning
[2010] showed that linear propositions correspond to session types, which
prescribe the observable behaviour of processes. Further, Carbone et al. [2018]
demonstrated that adopting devices from hypersequents [Avron 1991] shapes
proofs such that they correspond to the expected syntactic structure of
processes in the $\pi$-calculus. What remains is reconstructing the expected
metatheory of session types and the $\pi$-calculus. In particular, the hallmark
of session types, session fidelity, still has to be reconstructed: a
correspondence between the observable behaviours of processes and their session
types, in terms of labelled transitions.
  In this article, we present $\pi$LL, a new process calculus rooted in linear
logic. The key novelty of $\pi$LL is that it comes with a carefully formulated
design recipe, based on a dialgebraic view of labelled transition systems.
Thanks to our recipe, $\pi$LL offers the expected transition systems of session
types, which we use to establish session fidelity. We use $\pi$LL to carry out
the first thorough investigation of the metatheoretical properties enforced by
linear logic on the observable behaviour of processes, uncovering connections
with similarity and bisimilarity. We also prove that $\pi$LL and our recipe
form a robust basis for the further exploration of Proofs as Processes, by
considering different features: polymorphism, process mobility, and recursion.

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The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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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: solv-int
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The categories of this paper are: acc-phys