Logical handling of analogical proportions in commonsense and transductive reasoning

Analogies play an important role in many reasoning tasks. The presentation will introduce a recently proposed modeling for analogical proportions, i.e. statements of the form A is to B as C is to D, which put four situations into comparative relations. The logical representation used for encoding such proportions takes both into account what the four situations have in common and how they differ. Thanks to the use of a propositional logic modeling extended with suitable fuzzy logic connectives, the approach can deal with situations described by features that may be binary- or multiple-valued. Moreover, it will be shown that analogical proportions are related to other logically expressible proportions that are also of interest. The presentation will emphasize the interest of the approach for handling a large variety of forms of reasoning ranging from the solving of IQ tests, to case-based reasoning, interpolative and extrapolative reasoning, and transductive reasoning for classification. Potential for analogical argumentation will be also briefly discussed. The approach does not just rely on the exploitation of similarities between two cases, but rather takes advantage of the parallel made between a situation to evaluate or complete and three other situations.