The stepwise development of complex systems through various levels of abstraction is good practice in software and hardware design. However, the semantic link between these different levels is often missing. This book is intended as a detailed case study how such links can be established. It presents a theory of concurrent processes where three different semantic description methods are brought together in one uniform framework. Nets, terms and formulas are seen as expressing complementary views of processes, each one describing processes at a different level of abstraction.

• Petri nets are used to describe processes as concurrent and interacting machines which engage in internal actions and communications with their environment or user.

• Process terms are used as an abstract concurrent programming language. Due to their algebraic structure process terms emphasise compositionality, i.e. how complex terms are composed from simpler ones.

• Logical formulas of a first-order predicate logic, called trace logic, are used as a specification language for processes. Logical formulas specify safety and liveness aspects of the communication behaviour of processes as required by their users.

At the heart of this theory are two sets of transformation rules for the top-down design of concurrent processes. The first set can be used to transform logical formulas stepwise into process terms, and the second set can be used to transform process terms into Petri nets. These rules are based on novel techniques for the operational and denotational semantics of concurrent processes.