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Acting intelligently in dynamic environments involves anticipating surrounding processes, for example to foresee a dangerous situation by recognizing a process and inferring respective safety zones. Process recognition is thus key to mastering dynamic environments including surveillance tasks. In this paper, we are concerned with a logic-based approach to process specification, recognition, and interpretation. We demonstrate that linear temporal logic (LTL) provides the formal grounds on which processes can be specified. Recognition can then be approached as a model checking problem. The key feature of this logic-based approach is its seamless integration with logic inference which can sensibly supplement the incomplete observations of the robot. Furthermore, logic allows us to query for process occurrences in a flexible manner and it does not rely on training data. We present a case study with a robotic observer in a warehouse logistics scenario. Our experimental evaluation demonstrates that LTL provides an adequate basis for process recognition.