Conditional reasoning and relevance

Abstract

The Weak Completion Semantics is a computational and nonmonotonic cognitive theory based on the three-valued logic of Łukasiewicz. It has been applied to adequately model – among others – the suppression task, the selection task, syllogistic reasoning, and conditional reasoning. In this paper we investigate the case where the antecedent of a conditional is true, but its consequent is unknown. We propose to apply abduction in order to find an explanation for the consequent. This allows to derive new conditionals which are necessarily true. But it also leads to two problems, viz. that consequents should not abduce themselves and that the antecendent of a conditional should be relevant to its consequent. We propose solutions for both problems