Complex Systems and Cognitive Processes

This volume describes our intellectual path from the physics of complex sys­ tems to the science of artificial cognitive systems. It was exciting to discover that many of the concepts and methods which succeed in describing the self­ organizing phenomena of the physical world are relevant also for understand­ ing cognitive processes. Several nonlinear physicists have felt the fascination of such discovery in recent years. In this volume, we will limit our discussion to artificial cognitive systems, without attempting to model either the cognitive behaviour or the nervous structure of humans or animals. On the one hand, such artificial systems are important per se; on the other hand, it can be expected that their study will shed light on some general principles which are relevant also to biological cognitive systems. The main purpose of this volume is to show that nonlinear dynamical systems have several properties which make them particularly attractive for reaching some of the goals of artificial intelligence. The enthusiasm which was mentioned above must however be qualified by a critical consideration of the limitations of the dynamical systems approach. Understanding cognitive processes is a tremendous scientific challenge, and the achievements reached so far allow no single method to claim that it is the only valid one. In particular, the approach based upon nonlinear dynamical systems, which is our main topic, is still in an early stage of development.

1 Introductory Concepts.- 1.1 Complex Systems and Self-organization.- 1.2 Self-organization in Artificial Systems.- 1.3 Cognitive Processes in Artificial Systems.- 1.4 Metaphors of the Cognitive Sciences.- 2 The Dynamical Systems Approach to Artificial Intelligence.- 2.1 Introduction.- 2.2 Dynamical Systems, Attractors and Meaning.- 2.3 Neural Networks.- 2.4 The Relationship with Classical AI.- 3 Dynamical Behaviour of Complex Systems.- 3.1 Introduction.- 3.2 One-Dimensional Dynamical Systems.- 3.3 Two-Dimensional Dynamical Systems.- 3.4 Cellular Automata.- 3.5 The Life Game.- 3.6 Random Boolean Networks.- 3.7 Computation in Reaction-Diffusion Systems.- 4 Homogeneous Neural Networks.- 4.1 Introduction.- 4.2 The Hopfield Model.- 4.3 Modifications of the Hopfield Model.- A4.1 Non-Deterministic Dynamics of the Model.- A4.2 Memorization and Recognition of Two States.- 5 Network Structure and Network Learning.- 5.1 Introduction.- 5.2 Layered Networks.- 5.3 Back-Propagation Algorithms.- 5.4 Self-organization and Feature Extraction.- 5.5 Learning in Probabilistic Networks.- 5.6 Unsupervised Learning.- A5.1 The Learning Algorithm for the Boltzmann Machine.- 6 Dynamical Rule Based Systems.- 6.1 Introduction.- 6.2 Classifier Systems and Genetic Algorithms.- 6.3 The Equations of Classifier Systems.- 6.4 The Dynamics of Classifier Systems.- 6.5 Classifier Systems and Neural Networks.- A6.1 Implicit Parallelism.- 7 Problems and Prospects.- 7.1 Introduction.- 7.2 Knowledge Representation.- 7.3 The Role of Dynamics.- 7.4 On the Limits of the Dynamical Approach.- References.