Fuzzy temporal reasoning on causal models

Abstract

Temporal reasoning should play a very important role in many knowledge-intensive problem solving activities and, in particular, in the diagnostic process. In a previous article we proposed a categorical approach to deal with time in diagnostic reasoning based on causal (deep) models. Such an approach allows us to verify whether the observation and temporal location of a set of findings is consistent with a given causal evolution (path in a causal network) and, thus, with the solution to a diagnostic problem. In this article we propose an extension of the temporal reasoning process towards fuzzy reasoning. In particular, we consider the case where the temporal location of observed findings is not given in a crisp way, but only the possibility and necessity distributions of each finding is known. As a consequence, we have introduced some fuzzy criteria to verify the temporal consistency of a causal explanation, defining, in particular, a mechanism to evaluate the compatibility degree between a causal explanation and a set of findings.