On informativeness and reducibility in competence models

Abstract

Informativeness refers to the extent to which competence states can be inferred from knowledge states by using the equivalence relation induced by problem functions. This concept is closely tied to the minimal or maximal elements within the equivalence classes of skills. This paper primarily explores, within the framework of conjunctive competence models, the relationship between informativeness and floors, which are defined as the greatest lower bounds within these equivalence classes. To represent informativeness, an order embedding between two ordered sets is constructed. Additionally, the study extends its analysis to disjunctive competence models and general competence models. Building on this foundation, we investigate the properties of reducible conjunctive and disjunctive competence models, presenting a method for deriving a unique irreducible domain restriction.