Orthogonal Relations for Reasoning about Abstract Events

As systems become increasingly complex, event abstraction becomes an important issue in order to represent interactions and reason at the right level of abstraction. Abstract events are collections of more elementary events, that provide a view of the system execution at an appropriate level of granularity. Understanding how two abstract events relate to each other is a fundamental problem for knowledge representation and reasoning in a complex system. In this paper, we study how two abstract events in a distributed system are related to each other in terms of the more elementary causality relation. Specifically, we analyze the ways in which two abstract events can be related to each other orthogonally, that is, identify all the possible mutually independent relations by which two such events could be related to each other. Such an analysis is important because all possible relationships between two abstract events that can exist in the face of uncertain knowledge can be expressed in terms of the irreducible orthogonal relationships.