Structures In Systems 2: Viewpoint Cohomology Of General Systems

This paper introduces new homology and cohomology functors designed to analyze a broad range of logical systems including representations of enterprise information systems. Such systems contain nested relations and are a class of higher order logic. The homology and cohomology augment simplex constructions with ideas of type extensions to capture the logic of the system. Here logical systems, including large-scale information systems, have a class of derived objects called scenarios that give the connective logic of the system. Scenarios have a secondary logic derived from the underlying business rules of the enterprise. A viewpoint is a flexible classification logic which creates proxy variables so that the (co)homology functors can be applied to the secondary (and higher) scenario logics but with different (but functionally related) variables. These viewpoint (co)homologies can then analyze structures in emergent phenomena that reflect structures in the logic of the original system.