Probabilistic implication bases in FCA and probabilistic bases of GCIs in

Abstract

A probabilistic formal context is a triadic context the third dimension of which is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications with respect to probabilistic formal contexts, and provides a construction for a base of implications the probabilities of which exceed a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coincide. Furthermore, the results are extended towards the lightweight description logic with probabilistic interpretations, and a method for computing a base of general concept inclusions the probabilities of which are greater than a pre-defined lower bound is proposed. Additionally, we consider so-called probabilistic attributes over probabilistic formal contexts, and provide a method for the axiomatization of implications over probabilistic attributes.