The mechanisms of analogical learning
Similarity and analogical reasoning
Learning and reasoning by analogy
Communications of the ACM
Case-Based Approximate Reasoning (Theory and Decision Library B)
Case-Based Approximate Reasoning (Theory and Decision Library B)
Journal of Artificial Intelligence Research
A logical approach to reasoning by analogy
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 1
Logical proportions: typology and roadmap
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
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Analogy plays a very important role in human reasoning. In this paper, we study a restricted form of it based on analogical proportions, i.e. statements of the form a is to b as c is to d. We first investigate the constitutive notions of analogy, and beside the analogical proportion highlights the existence of two noticeable companion relations: one that is just reversing the change from c to d w. r. t. the one from a to b, while the last one called paralogical proportion expresses that what a and b have in common, c and d have it also. Characteristic postulates are identified for the three types of relations allowing to provide set and Boolean logic interpretations in a natural way. Finally, the solving of proportion equations as a basis for inference is discussed, again emphasizing the differences between analogy, reverse analogy, and paralogy, in particular in a three-valued setting, which is also briefly presented.