Connections and Dissimilarities Among Formal Concept Analysis, Knowledge Space Theory and Cognitive Diagnostic Models in a Systemic Perspective

Abstract

In the early eighties of the last century three theories were independently developed in the fields of information science, mathematical psychology and cognitive psychology. In 1982 Rudolph Wille conceptualized a principled way of deriving a concept hierarchy from a collection of objects and their properties: the Formal Concept Analysis. Such representation draws upon the order theory developed in 1937 by Birkhoff about the one-to-one correspondence between distributive lattices and partial orders. In 1985 Jean Claude Falmagne and Jean-Paul Doignon, starting from Birkhoff’s theorem, developed a theory to represent the prerequisite relations among sets of problems in the field of knowledge assessment: The Knowledge Space Theory. In 1983 Kikumi Tatsuoka introduced the concept of a Q-Matrix defining the basis for the development of a skill based way for cognitive diagnosis: The Cognitive Diagnostic Models. It is an interesting issue how, so far, only few attempts to highlight similarities among these theories have been carried out. This research is aimed at pinpointing some of the main deterministic and probabilistic concepts that, even if named differently, are shared by the three theories.