Congruence from the Operators Point of View: Compositionality Requirements on Process Semantics

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.

💡 Research Summary

The paper tackles a fundamental quality of behavioural semantics: congruence with respect to the standard process operators of a process algebra. Traditionally, this property has been ensured by devising rule formats for transition system specifications (TSS) that guarantee any semantics defined by such rules is a congruence. While effective, rule‑format approaches often impose uniform syntactic constraints that are either overly restrictive or unnecessarily generic for particular operators.
To overcome these limitations, the authors adopt an orthogonal, operator‑centric methodology. For each operator they consider—action prefix (a·_), alternative composition (P+Q), two restriction operators (