Independence Relations in Probabilistic Logic (Extended Abstract)

In “standard” probability theory, one lists all events that are logically possible, and then places a normalized measure over them. This scheme is rather dry. It may happen that the list of possible events is encoded through logical sentences, and one must employ logical reasoning to determine which events are included in probabilistic assessments. It may also happen that probabilistic assessments are intervalor set-valued. By following these steps we obtain the typical framework of probabilistic logics, where inferences may be either consistent (and then they may be interval-/set-valued) or inconsistent [3, 4, 12, 10]. Despite this level of flexibility, most probabilistic logics are less general than “standard” probability theory in one aspect: while the latter devotes meticulous attention to the concept of (conditional) independence, the former pays little tribute to that concept. It is only in very general first-order logics that one finds definitions of independence [2], and even there the concept of independence is not discussed in any detail.