A mathematical formulation of intelligent agents and their activities



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University of Cape Town

The task of optimising a collection of objective functions subject to a set of constraints is as important to industry as it is ubiquitous. The importance of this task is evidenced by the amount of research on this subject that is currently in progress. Although this problem has been solved satisfactorily in a number of domains, new techniques and formalisms are still being devised that are applicable in fields as diverse as digital filter design and software engineering. These methods, however, are often computationally intensive, and the heavy reliance on numeric processing usually renders them unintuitive. A further limitation is that many of the techniques treat the problem in top-down fashion. This approach often manifests itself in large, complex systems of equations that are difficult to solve and adapt. By contrast, in a bottom-up approach, a given task is distributed over a collection of smaller components. These components embed behaviour that is determined by simple rules. The interactions between the components, however, often yield behaviour, the complexity of which surpasses what can be captured by the systems of equations that arise from a top-down approach. In this dissertation, we wish to study this bottom-up approach in more detail. Our aim is not to solve the optimisation problem, but rather, to study the smaller components of the approach and their behaviour more closely. To model the components, we choose intelligent agents because these represent a simple yet effective paradigm for capturing complex behaviour with simple rules. We provide several representations for the agents, each of which enables us to model a different aspect of their behaviour. To formulate the representations, we use techniques and concepts from fields such as universal algebra, order theory, domain theory and topology. As part of the formulation we also present a case study to demonstrate how the formulation could be applied.

Includes bibliography: leaves 119-126.