Discussion

Abstract

In this chapter some additional topics related to abstraction in general are discussed. Some interesting extensions of the $\mathcal KRA$ model, suggesting possible future improvements, are briefly reviewed. The fact that abstraction may be the basis for analogical and metaphorical reasoning, for creating caricatures and archetypes, as well as the main tool to form categories is discussed. Since virtually all views of abstraction share the idea that abstraction should bring some advantage in terms of simplification, some generic considerations on its effective computational speedup are given, especially in the case of exponential problems. A possible direction of extension of the $\mathcal KRA$ model is to include stochastic environments, where the application of an operator does not generate a deterministic abstract state, but only a probability distribution over a subset of states. Another extension, which adds an ontology to the model, is described; it supports the definition of different types of objects to be abstracted in a controlled way, and has been applied with success to problems of model-based diagnosis.