A New Perspective on Analogical Proportions

Analogical proportions are statements of the form “a is to b as c is to d”. They have known a revival of interest after they have been formalized and used in analogical inference. In particular their meaning has been made clear through a logical modeling. The paper shows that they are closely related to the heart of the reasoning process, since dichotomic trees built from pairs of mutually exclusive properties have also a reading in terms of Boolean analogical proportions. This provides a link between analogy and logically expressed taxonomies. Moreover, this gives birth to noticeable opposition structures, and can be also related to formal concept analysis.

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