Probabilistic Implicational Bases in FCA and Probabilistic Bases of GCIs in EL
Francesco Kriegel · 2015
Abstract. A probabilistic formal context is a triadic context whose third dimen-sion is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications, and provides a construction for a base of implications whose probability satisfy a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coin-cide, and cannot be compared. Furthermore, the results are extended towards the light-weight description logic EL ⊥ with probabilistic interpretations, and a method for computing a base of general concept inclusions whose probability fulfill a certain lower bound is proposed.