Concurrent Realizability on Conjunctive Structures

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).