Communication, and concurrency with logic-based restriction inside a calculus of structures

TL;DR

This paper develops a logical framework within the Calculus of Structures to model process algebra operations, including restriction, enabling logical proof-search to solve reachability problems in a process algebra that extends Milner CCS.

Contribution

It introduces a purely logical account of process algebra operations with restriction inside a deep inference system, connecting proof-search with process algebra reachability.

Findings

Logical system models restriction in process algebra

Proof-search solves reachability in an extended process algebra

Subsystems include significant parts of Milner CCS

Abstract

It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing a correspondence between proof-search of a logical system and computations in a process algebra. We give a purely logical account of a process algebra operation which strictly includes the behavior of restriction on actions we find in Milner CCS. This is possible inside a logical system in the Calculus of Structures of Deep Inference endowed with a self-dual quantifier. Using proof-search of cut-free proofs of such a logical system we show how to solve reachability problems in a process algebra that subsumes a significant fragment of Milner CCS.