Abstract
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.
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Prade, H., Richard, G. (2009). Analogy, Paralogy and Reverse Analogy: Postulates and Inferences. In: Mertsching, B., Hund, M., Aziz, Z. (eds) KI 2009: Advances in Artificial Intelligence. KI 2009. Lecture Notes in Computer Science(), vol 5803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04617-9_39
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DOI: https://doi.org/10.1007/978-3-642-04617-9_39
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