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Existing approaches for business process mining cannot satisfy Real-Time Enterprise (RTE) goals, such as time-based competition. To support RTE requirements we propose a Process Learning System (PLS) that is capable of learning business processes from a few observed traces and do this in a timeframe that is close to the actual time for completing the process. Unlike existing approaches PLS employs a rich process model that facilitates "guessing" business processes, utilizes domain-specific knowledge captured by activity and resource ontologies, ensures that learned processes comply with specified business rules, and optimizes them to reduce required cost and time. In this paper we focus on the architecture of PLS, and describe the functionality and algorithms employed by key PLS components. We use examples from initial experiments involving learning of processes that assemble complex products from specialized parts.