Abstract
The paper studies inverse casual reasoning which derives possible causes from uncertain causation knowledge and evidence(results), and proposes two new approaches, one based on probability theory and the other on possibility theory. There are some conventional approaches that can deal with the inverse causal reasoning with uncertain evidence. Reasoning with Jeffrey's rule, approximate reasoning with subjective Bayesian method, and Bayesian network approach are those based on probability theory. As for possibility theory, inverse problem of fuzzy relational equations and a method employing the idea of Jeffrey's rule could be applicable. However, it has been designated that conditional probabilities and conditional possibilities, one of which are used in all approaches mentioned above, are inappropriate to express uncertainty of causation recognized by human, and that conditional causal probabilities and conditional causal possibilities should be used instead. The paper first discusses conventional approaches of inverse causal reasoning from uncertain evidence with conditional probabilities and conditional possibilities. Then, it proposes two new approaches, one employs conditional causal probabilities and the other conditional causal possibilities. These two approaches are developed based on the same idea, though they use different measures meaning probabilities and possibilities to express the uncertainty. It also discusses how to give probability or possibility data when the proposed approaches are applied to inverse causal problems.
