Temporal factorisation: Realisation of mediating state properties for dynamics

Temporal factorisation is a principle underlying approaches to dynamics used within many disciplines. According to this principle any temporal relationship of the form ‘past pattern implies future pattern’ can be factorised into a relationship of the form ‘past pattern implies present state’ and a relationship of the form ‘present state implies future pattern’. To enable this, the principle postulates the existence of certain mediating state properties in the present state. In this paper the question is addressed whether and how a postulated mediating state property relates to other state properties in the (present) state in which they occur. In particular, the situation is analysed that realisers exist: other state properties or combinations thereof that co-occur with the mediating state property in states. This analysis provides a conceptual framework covering various concepts and themes that usually are considered totally different and unrelated, such as, the notion of differential equation in Mathematics, the notions of transition system and rule-based system in Computer Science, Cognitive Science and Artificial Intelligence, and the notion of reduction in Cognitive Science and Philosophy of Science.