Logic of multicomponent systems and a combinatorial model of causal relationships

Abstract

The effects which are typical for multicomponent systems, i.e. for objects composed of parts, are studied from the logical standpoint. Possible types of the formal relationship between a property of an object as a whole (called here a “hyperproperty”) and a property of its separate parts or elements are analyzed. Simple standard forms of such relationships are isolated (“separable hyperproperties”). The deviations from these standard forms are described in terms of intrasystem interactions between elements or parts. The investigated formal types of the influence that an element property has on a system property are interpreted in causal terms. This provides a basis for the formal analysis of the “cause-consequence dependence” notion in the framework of a simple combinatorial model of the dependence between events.