In the theory of denotational semantics of programming languages (also called Domain theory, pioneering work due to Dana S. Scott, a Turing Award Winner), various kinds of systems of information and associated partial orders (domains) together with Scott continuous functions have been extensively studied by many authors. A well-known corresponding is that there is a bijection between Scott's information systems and Scott domains.
As a generalization of Scott's information systems, an event structure is a models of some process as events (for example, Petri net) constrained by relations of consistency and enabling. The canonical event domain of an event structure is a Scott domain with property I (called SI-domain for short). The reverse holds when it is a DI-domain. However, it is not true that any SI-domain can be viewed as a canonical event domain. For example, the diamond lattice is not a canonical event domain.
In this talk, we will further study the relation between event structures and domains. We will give new approaches to represent domains by event structures and reveal the category relationships among event domains.