  We consider approaches for causal semantics of Petri nets, explicitly
representing dependencies between transition occurrences. For one-safe nets or
condition/event-systems, the notion of process as defined by Carl Adam Petri
provides a notion of a run of a system where causal dependencies are reflected
in terms of a partial order. A well-known problem is how to generalise this
notion for nets where places may carry several tokens. Goltz and Reisig have
defined such a generalisation by distinguishing tokens according to their
causal history. However, this so-called individual token interpretation is
often considered too detailed. A number of approaches have tackled the problem
of defining a more abstract notion of process, thereby obtaining a so-called
collective token interpretation. Here we give a short overview on these
attempts and then identify a subclass of Petri nets, called structural conflict
nets, where the interplay between conflict and concurrency due to token
multiplicity does not occur. For this subclass, we define abstract processes as
equivalence classes of Goltz-Reisig processes. We justify this approach by
showing that we obtain exactly one maximal abstract process if and only if the
underlying net is conflict-free with respect to a canonical notion of conflict.
