Possibilistic Causality Consistency Problem Based on Two Different Causal Models and Properties of Its Solutions

Abstract

Conditional Causal Probability(CCPR)and Conditional Causal Possibility(CCPO)have been proposed to express exact degrees of uncertainty in causalities, and some reasoning methods have been studied to obtain probablities or possibilities of unknown events under the condition that some events are known. CCPR is defined as a conditional probability of a Causation event conditioned by the Cause event. Causation event is an "event that a cause actually causes an effect." CCPO is a conditional possibility of a Causation event conditioned by the Cause event. The paper proposes to classify causal models using Causation events into two types-symmetrically valued and asymmetrically valued causal models-depending on the properties of variables, which take an event as their value. It also shows that the relations between conventional conditional possibilities and CCPOs are different between these models. Then, it discusses solutions and their properties of a Causality Consistency Problem using a hierarchical causal network, which is a problem to obtain the possibilities of combinations of values of arbitrarily chosen unknown variables, when values of some other variables are known. The discussion of the two different models can be conducted in the same way, because it is possible using conditional possibilities derived from CCPOs except proofs of some propositions. The proposed Causality Consistency Problem is a general one including Inverse Causality Problem and Causality Analysis Problem studied in the previous research.