Concurrent Realizability on Conjunctive Structures

TL;DR

This paper explores axiomatisations of concurrent computation through proof theory and realizability, redefining concurrent realizability with a $ ext{pi}$-calculus and conjunctive structures, focusing on non-replicative processes and linear logic.

Contribution

It introduces a new framework for concurrent realizability using conjunctive structures and a $ ext{pi}$-calculus variant, extending prior realizability models to concurrency.

Findings

Redefinition of concurrent realizability with $ ext{pi}$-calculus

Introduction of conjunctive structures for realizability

Encoding realizers into algebraic structures without replication

Abstract

The point of this work is to explore axiomatisations of concurrent computation using the technology of proof theory and realizability. To deal with this problem, we redefine the Concurrent Realizability of Beffara using as realizers a $\pi$-calculus with global fusions. We define a variant of the Conjunctive Structures of \'E Miquey as a general structure where belong realizers and truth values from realizability. As for Secuential Realizability, we encode the realizers into the algebraic structure by means of a combinatory presentation, following the work of Honda & Yoshida. In this first work we restricted to work with the $\pi$-calculus without replication and its corresponding type system is the multiplicative linear logic (MLL).