  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.
