Possibilistic causality consistency problem based on asymmetrically-valued causal model

The paper addresses uncertain reasoning based on causal knowledge given by two layered networks, where nodes in one layer express possible causes and those in the other are possible effects. Uncertainties of the causalities are given by conditional causal possibilities, which were proposed to express the exact degrees of possibility of causalities. The expression of the uncertainty also has an advantage over the conventional conditional possibilities in the number of possibilistic values that should be given as a priori knowledge. The number of conditional causal possibilities given as knowledge is far smaller than that of conventional conditional possibilities.The paper starts with the definition of a causal model called asymmetrically-valued causal model. The conditional causal possibilities are defined on the causal model, and their mathematical properties are discussed. Then, the paper defines the possibilistic causality consistency problem based on the proposed model and shows how to solve the problem. The discussed problem is one to calculate the conditional possibility of a hypothesis about presence and absence of unknown events when the states of some other events are known.