Congruence from the Operator's Point of View: Compositionality Requirements on Process Semantics

TL;DR

This paper proposes a novel approach to ensuring process semantics are congruences for process operators by restricting sublanguages of Hennessy-Milner logic, rather than developing rule formats.

Contribution

It introduces a new method focusing on modal logic restrictions to guarantee congruence for various process operators, offering an orthogonal alternative to traditional rule format approaches.

Findings

Identifies classes of modal logic restrictions ensuring congruence

Applies approach to action prefix, composition, and parallel operators

Provides a broader class of congruences for process semantics

Abstract

One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition system specifications that define process algebras. In this paper we suggest a novel, orthogonal approach. Namely, we focus on a number of process operators, and for each of them attempt to find the widest possible class of congruences. To this end, we impose restrictions on sublanguages of Hennessy-Milner logic, so that a semantics whose modal characterization satisfies a given criterion is guaranteed to be a congruence with respect to the operator in question. We investigate action prefix, alternative composition, two restriction operators, and parallel composition.