Explanatory Relations Based on Mathematical Morphology
Using mathematical morphology on formulas introduced recently by Bloch and Lang (Proceedings of IPMU'2000) we define two new explanatory relations. Their logical behavior is analyzed. The results show that these natural ways for defining preferred explanations are robust because these relations satisfy almost all postulates of explanatory reasoning introduced by Pino-PErez and Uzcategui (Artifical Intelligence, 111:131-169, 1999). Actually, the first explanatory relation is Explanatory-Rational. The second one is not even Explanatory-Cumulative but it satisfies new weak postulates.