A Process Calculus with Logical Operators

TL;DR

This paper introduces a process calculus called CLL that integrates logical operators into process specifications, providing a formal framework with behavioral semantics and an axiomatic system for reasoning about combined specifications.

Contribution

It develops a process calculus for Logic LTSs with logical operators, including a behavioral theory and a sound, complete axiomatic system.

Findings

Defined a process calculus CLL with logical operators

Established a behavioral refinement relation via ready simulation

Provided a sound and complete axiomatic system for CLL

Abstract

In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS 373(1-2):19-40; Inform. & Comput. 208:845-867]. In contrast with usual LTS, two logical constructors $\wedge$ and $\vee$ over Logic LTSs are introduced to describe logical combinations of specifications. Hitherto such framework has been dealt with in considerable depth, however, process algebraic style way has not yet been involved and the axiomatization of constructors over Logic LTSs is absent. This paper tries to develop L\"{u}ttgen and Vogler's work along this direction. We will present a process calculus for Logic LTSs (CLL, for short). The language CLL is explored in detail from two different but equivalent views. Based on behavioral view, the notion of ready simulation is adopted to formalize the refinement relation, and the behavioral theory is developed. Based on proof-theoretic view, a sound and ground-complete axiomatic system for CLL is provided, which captures operators in CLL through (in)equational laws.