Causal ordering and the symmetry problem of basic linear systems

Abstract

Abstract This paper treats causal ordering in the framework of mathematical general systems theory. Due to its importance causal ordering has been much discussed, however, it has not hitherto been formulated as a system theoretic property. This paper formulates causal ordering as one of the proper system theoretic properties that should be characterized only by the behaviour of a system. In particular, for a general system S given by a binary relation over system objects X ajnd Y. we say there exists a causal ordering from X to Y if X is non-trivially related to Y and if it is possible to decompose S into a class of functional subsystems where each functional subsystem expresses a determinism from events of X to events of Y such that an event of Y occurs after an event of X. Based on this formulation, Simon's, symmetry problem of causal ordering, that is the mterehangeability problem of a cause and an effect, is considered. Characterizations of symmetry and asymmetry of causal. ordering are given for basi...