Proof Nets for PiL (Full Version)

2026-05-14

AI Summary

This work addresses the lack of a concise and canonical logical representation for π-calculus processes by proposing a proof net system based on PiL logic—an extension of first-order multiplicative additive linear logic. By introducing novel operators to shallowly encode π-calculus processes, the paper establishes the first proof net theoretical framework for PiL, complete with a correctness criterion, a sequentialization algorithm, and a proof translation mechanism. This approach not only provides a logical characterization of π-calculus processes but also yields a unique and canonical representation for sequent calculus derivations modulo rule permutation equivalences, thereby effectively resolving the problem of derivation equivalence.

Abstract

We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the π-calculus as formulas. We provide correctness criterion, sequentialization procedure, and a proof translation algorithm. We show that proof nets provide a canonical representation of sequent calculus derivations modulo rule permutations.

Problem

• proof nets
• PiL
• linear logic
• π-calculus
• sequent calculus

Innovation

• proof nets
• PiL
• π-calculus
• linear logic
• canonical representation