Polishing diamonds in OWL 2

A recurrent pattern in the representation of actions and processes is the notion of exchange. It is a concept primarily characterised by a structure of processes or actions, rather than inherent properties, but has a strong ontological flavour. Exchange is furthermore governed by reciprocity, reflected by the way in which roles are constrained.
Representing exchange and other structured objects in an ontology poses a number of conceptual and technical problems. While these concepts require a diamond like structure, DLs are generally restricted to tree structures only. Constraints on the identity of the individuals that fill the roles in e.g. transactions cannot be enforced directly in the A-Box. In this paper we present a knowledge pattern and methodology for approximating such structures.