Competence-Based Skill Functions and Minimal Sets of Skills

Abstract

As we know, there is some relationship, such as precedence relation, among skills. Each precedence relation induces a competence structure. Thus, we study competence-based skill functions, which rely on competence structures and go from somethings observable to somethings invisible. Conversely, competence-based problem functions go from somethings invisible to somethings ob-servable. In fact, these two dual types of functions based on competence structures are symmetry. Remarkably, there are two kinds of special competence-based skill functions: one is disjunctive, while the other is conjunctive. The former delineates knowledge spaces, which are symmetrical to simple closure spaces delineated by the latter. Based on these facts, we shows some theoretical results on competence-based skill functions, then design the corresponding algorithms for delineating knowledge structures. Sometimes for competence-based skill functions, some skills are maybe reducible. Thus, we discuss what kind of skills are reducible and obtain sufficient and some necessary conditions for skills being reducible for competence-based skill functions. Based on this, we design algorithms to reduce reducible skills and get minimal sets of skills. By comparison, for competence-based skill functions, we can find minimal sets of skills with the smallest cardinality whenever sets of skills are finite. For each algorithm, we take a corresponding example to illustrate the detailed procedure.