Approximate reasoning mechanism: internal, external, and hybrid

摘要

We suggest an input-output system point of view of the mechanism in generalized modus ponens (GMP). The antecedent and consequent in the premise are treated as an input-output pair. The other premise and the conclusion are treated as another pair. It is suggested that the two pairs are related to each other in the sense that they are generated by the same system. With the input-output system aspect, we propose to categorize the previous approximate reasoning mechanism to be either internal or external. More insights of the internal and external mechanism are explored. In addition, a new hybrid mechanism is introduced for the OMP. We suggest a way to justify that one pair is reasoned based purely on the other. This is through the comparison of the truth values of the two pairs. The hybrid mechanism preempts that the truth value of one input-output pair, which also can be viewed as a fuzzy inference, should be identical to the other. This is coined as the Principle of Equal Truth Value (PETV). Some GMP performance, which people would often expect in a realistic GMP but is never rigorously guaranteed in other mechanism, is a natural consequence of the hybrid mechanism. Another interesting result of the hybrid mechanism is that it not only indicates what can be achieved, but also what can not be done in the reasoning. This appears to be more aligned with human experience: If the basis of reasoning (in the GMP, it is Premise 2) is too far away from the occurrence (i.e., Premise 1), then there is nothing one can say about the consequence (i.e., Conclusion) due to the occurrence.