Working Papers of the 1 st International Workshop on S imilarity and A nalogy - based M ethods in AI

Analogies play an important role in many reasoning tasks. In this paper, we survey a recently proposed modeling for an analogical proportion, i.e. a statement of the form “A is to B as C is to D”, and its diverse applications. 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 Boolean modeling extended with suitable fuzzy logic connectives, the approach can deal with situations described by features that may be binary or multiple-valued. It is shown that analogical proportion is a particular case of a more general concept, namely logical proportion. Among the 120 existing logical proportions, we single out four proportions (including the analogical proportion) for their remarkable properties. We emphasize the interest of analogy-related logical proportions for handling a large variety of reasoning tasks, ranging from solving IQ tests, to transductive reasoning for classification, and interpolative and extrapolative reasoning. The approach does not just rely on the exploitation of similarities between two cases (as in casebased reasoning), but rather takes advantage of the parallel made between a situation to be evaluated or to be completed, with three other situations.