On Categorial Membership

International audienceWe investigate the family of concepts that an agent comes to knowthrough a set of defining features, and examine the role played by these features inthe process of categorization. In a qualitative framework, categorial membership isevaluated through an order relation among the objects at hand, which translates thefact that an object may fall more than another under a given concept. For conceptsdefined by their features, this global membership order depends on the degree withwhich each feature applies to the objects of the universe. The passage from theseindividual membership degrees to a global membership order poses a problemanalogous to vote aggregation in social choice theory. This similarity leads to anoriginal solution that is particularly well-adapted to the framework of cognitivepsychology. The resulting membership order extends to compound concepts, andprovides a good description of the guppy paradox and the conjunction effect

On the notion of concept II

International audienceIn 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