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Abstract:

So far, abstraction has been mainly investigated in problem solving tasks. In this paper, we are interested in the role of abstraction in representing and learning concepts (i.e., intensional descriptions of classes of objects). We propose a novel perspective on abstraction, originating from the observation that a conceptualization of a domain involves entities belonging to at least three levels. The fundamental level is the perception of the world, where concrete objects reside. For memorizing objects, some kind of structure, which describes objects and relations perceived in the world, is needed. Finally, to communicate with others, and also to perform reasoning, a language has to be used; the language allows both the world and theories about the world to be described intensionally. In previous approaches, abstraction has been frequently defined as a mapping between languages. Our main departure from this view is that abstraction is, originally, a mapping between views of the world, and that the modifications of the structure and of the language are side-effects, necessary to describe what happens at the level of the perceived world. Within the defined framework, we show how the abstraction process can be realized by means of a set of operators, and we formalize a constraint that abstraction mappings should satisfy in order to be useful for Machine Learning, i.e. preserving the generality relation among hypotheses. 1.

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