A Propositional Dynamic Logic for CCS Programs

Abstract

This work presents a Propositional Dynamic Logic in which the programs are CCS terms (CCS-PDL). Its goal is to reason about properties of concurrent systems specified in CCS. CCS is a process algebra that models the concurrency and interaction between processes through individual acts of communication. At a first step, we consider only CCS processes without constants and give a complete axiomatization for this logic, which is very similar to *-free PDL. Then, we proceed to include CCS processes with constants. In this case, we impose some restrictions on the form of the recursive equations that can be built with those constants. We also give an axiomatization for this second logic and prove its completeness using a Fischer-Ladner construction. Unlike Concurrent PDL (with channels) [1,2], our logic has a simple Kripke semantics, a complete axiomatization and the finite model property.