BPMN 2.0 standard has a huge uptake in modelling business processes within the same organisation or collaborations involving multiple interacting participants. It results that providing a solid foundation to enable BPMN designers to understand their models in a consistent way is becoming more and more important. In our investigation we define and exploit a formal characterisation of the collaborations' semantics, specifically and directly given for BPMN models, to provide a classification of BPMN collaborations. In particular, we refer to collaborations involving processes with arbitrary topology, thus overcoming the well-structuredness limitations. The proposed classification is based on some of the most important correctness properties in the business process domain, namely safeness and soundness. We prove, with a uniform formal framework, some conjectured and expected results and, most of all, we achieve novel results for BPMN collaborations concerning the relationships between safeness and soundness, and their compositionality, that represent major advances in the state-of-the-art.
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