Abstract
Conditional probabilities are widely used, when we evaluate uncertainty of causalities. However, Peng & Reggia designate that conditional probability is different from the uncertainty of causation that we have in mind, since it is a probabilistic evaluation including events that the effect happens to be caused by another cause, not by the cause given as the condition. Thus they proposed causation event that the cause actually causes the effect, and conditional causal probability which is a conditional probability of causation event given the cause. They also applied them to an inverse problem of causalities, which is a problem to calculate the posterior probability that a given plural causes are arising, when a set of effects are observed. This paper proposes conditional causal possibility(CCP) which has similar semantics to the conditional causal probability, and describes the relation between CCP and conditional possibility(CP). It also studies methods to apply CP and CCP to an inverse problem of causalities, and indicates that improper cases may appear when CP is used and that they can be avoided if CCP is used instead.
