Categorisation: ALogical Approach to a Cognitive Problem

Abstract

In classical approach of categorization different problems arise. Non Monotonie Logic, Para-consistant logic Pseudo-consistant Logic, fuzzy set try to give answers for solving these problems. A "logical analysis" of the notions of "typicality" and "atypicality" is presented here in the ways opened by cognitive psychology, with the works of E. Rosch and other psychologists (J.-F. Le Ny), by philosophy (with Wittgenstein's "resemblance" and also with the old Aristotelian notion of "essence") and by logicians like Leibniz and Port-Royal in close connexion with linguistic expressions of naturallanguages. The formalism we propose is called "Logic for Determination of Objects" (LDO). It is developed inside the framework of the sound and general theory of operators of Curry's Combinatory Logic. LDO starts with a formaI relation between extension and intension of a concept. A concept is viewed, from Frege, as a function in the set of true-values. We introduce associated to a given concept(i) "the" typical object, which is an abstract object as weIl as "the best representative instance of the concept" and (ii) a deterrnination function which contributes to give information for referencing objects. The classical Predicate Calculus and classical Semantic Networks in Artificial Intelligence handle only completely determinate objects. In LDO, for a given concept, its extension contains indeterminate as weIl as more and less determinate instances of the concept and also occurrences (completely deterrninate instances) of the concept.