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arXiv · 2411.08847

Proofs as Execution Trees for the {\pi}-Calculus

Matteo Acclavio·Giulia Manara
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Abstract

In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent processes as formulas, and we interpret proofs as computations. For this purpose, we define a cut-free sequent calculus for an extension of first-order multiplicative and additive linear logic. This extension includes a non-commutative and non-associative connective to faithfully model the prefix operator, and nominal quantifiers to represent name restriction. Finally, we design proof nets providing canonical representatives of derivations up to local rule permutations.

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Matteo Acclavio, Giulia Manara. 2024-11-13. Proofs as Execution Trees for the {\pi}-Calculus. https://arxiv.org/abs/2411.08847

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