Independence and dependence between concepts or propositions and the measurement

This paper formalizes the independence-dependence relation between concepts or propositions based on probabilistic description logic and probabilistic logic, presents an approach of measurement for the relation by associating concepts or propositions to random variables, and proposes a metric for measuring the degree of independence-dependence between concepts or propositions by using Pearson product-moment correlation coefficient. The paper reveals the spectrum (continuum) of independence-dependence and seven mutually exclusive cases in the spectrum, pointing out that the spectrum is a completion to the subsumption relation for concepts or implication relation for propositions.