On the notion of concept II
Résumé
In this paper, we carry on with the analysis of constructible concepts initiated in [M. Freund, On the notion of concept 1. Artificial Intelligence 172 (2008) 570-590], and examine the key notions of categorization theory that are linked with category-based induction. In the main part of the article, we propose a reformulation of classical prototype theory using the framework of monotonic and non-monotonic logics. In this perspective, the classical notions of essence and intension are respectively interpreted as sets of necessary and defeasible consequences, giving rise to a relation ⊢ analogous to that of classical consequence, and a relation ∼ which behaves, relatively to ⊢, like a supraclassical rational inference relation. This formal analogy between the language of categorization theory and that of propositional logic reveals itself to be particularly useful when dealing with the problem of category-based induction.In this paper, we carry on with the analysis of constructible concepts initiated in [M. Freund, On the notion of concept 1. Artificial Intelligence 172 (2008) 570-590], and examine the key notions of categorization theory that are linked with category-based induction. In the main part of the article, we propose a reformulation of classical prototype theory using the framework of monotonic and non-monotonic logics. In this perspective, the classical notions of essence and intension are respectively interpreted as sets of necessary and defeasible consequences, giving rise to a relation ⊢ analogous to that of classical consequence, and a relation ∼ which behaves, relatively to ⊢, like a supraclassical rational inference relation. This formal analogy between the language of categorization theory and that of propositional logic reveals itself to be particularly useful when dealing with the problem of category-based induction.