  In this paper the correspondence between safe Petri nets and event
structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets
without self-loops, under the collective token interpretation. To this end we
propose a more general form of event structure, matching the expressive power
of such nets. These new event structures and nets are connected by relating
both notions with configuration structures, which can be regarded as
representations of either event structures or nets that capture their behaviour
in terms of action occurrences and the causal relationships between them, but
abstract from any auxiliary structure.
  A configuration structure can also be considered logically, as a class of
propositional models, or - equivalently - as a propositional theory in
disjunctive normal from. Converting this theory to conjunctive normal form is
the key idea in the translation of such a structure into a net.
  For a variety of classes of event structures we characterise the associated
classes of configuration structures in terms of their closure properties, as
well as in terms of the axiomatisability of the associated propositional
theories by formulae of simple prescribed forms, and in terms of structural
properties of the associated Petri nets.
