par Degreef, Eric;Doignon, Jean-Paul 
;Ducamp, André ;Falmagne, Jean-Claude
Référence Journal of mathematical psychology, 30, 3, page (243-256)
Publication Publié, 1986-09
;Ducamp, André ;Falmagne, Jean-Claude Référence Journal of mathematical psychology, 30, 3, page (243-256)
Publication Publié, 1986-09
Article révisé par les pairs
| Résumé : | Any element S in a family ψ of subsets of a finite set X can be specified by a sequence of statements such as: x ∈ S, y ∉ S, t ∉ S,..., z ε{lunate} S. This sequence can be coded as a "word" xyt...z and a complete set of such words forms a "descriptive language" for the family ψ. This class of languages is defined precisely, and some connections between such languages and families of sets are investigated. It is shown in particular that when ψ is closed under intersections and unions, and satisfies the topological condition known as T0, then ψ can be recovered exactly from any of its descriptive languages. These results have an application in the assessment of knowledge. In this framework, the set X is a set of questions, and any set S ∈ ψ represents a possible knowledge state, containing all the questions that some individual is capable of solving. A subclass of the descriptive languages are then the "assessment languages." Any such language defines a nonredundant algorithm for determining the knowledge state of any individual. © 1986. |
