On the Phenomenological Reconstruction of Complex Systems—The Scale-Free Conceptualization Hypothesis

Abstract

Phenomenological reconstruction of a complex system (CS) from collected and selected data allows us to work with formal models (representations) of the system. The task of building a qualitative model necessitates the formalization of relationships among observations and concrete features. Formal concept analysis can help to understand the conceptual structure behind these qualitative representations by means of the so-called concept lattices (CLs). The study of these kinds of semantic networks suggests that a strong relationship exists between its topological structure and its soundness/usefulness as a qualitative representation of the CS. The present paper is devoted to this question by presenting the so-called scale-free conceptualization hypothesis. The hypothesis claims that a scale-free distribution of node connectivity appears on the CL associated to complex systems (CLCS) only when two requirements hold: CLCS is useful both to represent qualitative and reliable attributes on the CS, as well as to provide a basis for (qualitatively) successfully reasoning about the CS. Experiments revealed that the topologies of CLCS are similar when the amount of information on the CS is sufficient, whereas it is different in other CLs associated to random formal contexts or to other systems in which some of the former requirements do not hold.