<p>In this paper, competence-based knowledge space theory (CbKST) is approached from the perspective of formal concept analysis (FCA). The aim is to visualize the relationship between knowledge structure and competence structure. The skill map is transformed into a formal context, and the methodology for constructing the concept lattice is provided. Within a concept lattice, each node, referred to as a concept, embodies a knowledge state and a competence state as its extension and intention, respectively. The favorableness of concept lattice is defined in terms of the effectiveness of skill learning, and the sufficient and necessary conditions for a favorable concept lattices are given. From the perspective of effective learning, we propose a precedence relation between skills to guide the recommendation of personalized learning schemes. Moreover, it is proved that on a favorable concept lattice, there is a learning path that adheres to the principle of step-by-step and easy-to-difficult.</p>