Hierarchical Modelling: A Systemic Framework

Erminia Vaccari, Maria D'Amato, and William Delaney

According to Steier [1992] one main difference between systems theorists and cyerneticians centers on what is offered as a main principle of systems theory, as put forth by systems theorists, for example, von Bertalanffy [1968], concerning the necessity of a particular form of relationship, namely that of hierarchy. The paper focuses on the necessity to represent hierarchy when modeling systems of organised complexity [Weaver 1948]. A model can be hierarchical in different senses, e.g.: ]

a) connections between certain sub-models may represent authority relations [Simon,1962] in the real system, whereby subordinate sub-models are controlled by higher level sub-models;

b) a sub-system, S, may be represented twice in a model, once by a sub-model representing S as a whole and once by a set of sub-models representing the constituent sub-systems of S.

Typically sub-models at different hierarchical levels will represent phenomena occurring on different time scales.

The possibility of representing hierarchy with different time scales permits modeling of: variable structure systems, i.e. systems having sub-systems which only exist under certain circumstances (as a function of the system dynamics, they go in and out of existence); systems whose law of behavior depends on (dynamically varying) conditions; systems whose organisation depends on dynamically varying conditions feedforward mechanisms whereby a change of a system's state in the present occurs as a function of some predicted future state emergent behaviours in that in the same model one represents both a sub-system S (by model M) and its sub-sub-systems SS(i) by sub-models MM(i). Following [Auger and Poggiale,1996], comparisons of results of M and MM(i) may evidence emergent phenomena. It is reasonable to assume that a useful representation of complex systems must be able to take into account a hierarchy of conceptual and physical processes. We will discuss the theoretical basis and the design criteria of a systemic framework supporting hierarchical modeling.

References

[Auger and Poggiale, 1996] Pierre Auger and Jean-Cristophe Poggiale. Aggregation, Emergence and Immergence in Hierarchically Organized Systems Proc. of the Third European Congress on Systems Science, pages43-45, Rome, October 1996

[Bertalanffy, 1968] Ludwig von Bertalanffy. General, System theory: Foundations, Developments Applications New York, George Brazillier ed

[Simon, 1962] Herbert Simon .The Architecture of Complexity. Proc. Am. Philos. Soc. , 106, 467

[Steier, 1992] Frederick Steier. Cybernetics as . . . Mutualling. Cybernetics & Human Knowing , 1, 2/3, 1992

[Weaver, 1948] Warren Weaver. Science and Complexity. American Scientist ,.36.