Production processes are nowadays fragmented across different companies and organized in global collaborative networks. This is the result of the first wave of globalization that, among the various factors, was enabled by the diffusion of Internet-based Information and Communication Technologies (ICTs) at the beginning of the years 2000. The recent wave of new technologies possibly leading to the fourth industrial revolution – the so-called Industry 4.0 – is further multiplying opportunities. Accessing global customers opens great opportunities for organizations, including small and medium enterprises (SMEs), but it requires the ability to adapt to different requirements and conditions, volatile demand patterns and fast-changing technologies. Regardless of the industrial sector, the processes used in an organization must be compliant to rules, standards, laws and regulations. Non-compliance subjects enterprises to litigation and financial fines. Thus, compliance verification is a major concern, not only to keep pace with changing regulations but also to address the rising concerns of security, product and service quality and data privacy. The software, in particular process automation, used must be designed accordingly. In relation to process management, we propose a new way to pro-actively check the compliance of current running business processes using Descriptive Logic and Linear Temporal Logic to describe the constraints related to data. Related algorithms are presented to detect the potential violations.