From equations to patterns: Logic-based approach to general systems theory

Abstract

Many complex self-organizing systems may not be easily modeled with the help of differential equations. Modern studies in complexity generated new kinds of modeling paradigms such as Cellular Automata (CA), Boolean Networks, and Multiagent Systems. Such models are built from large numbers of interacting units with simple behavior defined in terms of production rules. These models are capable of reproducing unexpected complex organization patterns where the character of the organization could not be derived from the character of the rules defining the behavior of units. Organization that is not evident from the dynamic rules is called emergent . The existence of emergent organization demonstrates the inadequacy of the traditionally accepted association of systems organization with the dynamic equation of the system. The main objective of the paper is to describe new General Systems Theory (GST) framework that gives appropriate account of new dimensions of organization and accommodates new approaches to modeling of complex adaptive systems (CAS). To describe system states and state sequences we use concept model from formal semantics. Dynamics of a system are described with the help of patterns or production rules. The isomorphism of systems is naturally represented as model isomorphism. The organization of a system is a set of formulae with free variables, which have interpretation on the models that represent the system. The framework introduced here is developed as a part of our eco-modeling project. We also discuss the architecture of ecological simulator, LEM (Logic for Eco-Modeling), and its implementation in Visual Prolog that serves as an example of practical application of the framework.