In the last decade, with the expansion of organizational scope and the tendency for outsourcing, there has been an increasing need for Business Process Integration (BPI), understood as the sharing of data and applications among business processes. The research efforts and development paths in BPI pursued by many academic groups and system vendors, targeting heterogeneous system integration, continue to face several conceptual and technological challenges. This article begins with a brief review of major approaches and emerging standards to address BPI. Further, we introduce a rule-driven messaging approach to BPI, which is based on the harmonization of messages in order to compose a new, often cross-organizational process. We will then introduce the design of a temporal first order language (Harmonized Messaging Calculus) that provides the formal foundation for general rules governing the business process execution. Definitions of the language terms, formulae, safety, and expressiveness are introduced and considered in detail.
