Homogenous and heterogeneous logical proportions

Abstract : Commonsense reasoning often relies on the perception of similarity as well as dis- similarity between objects or situations. Such a perception may be expressed and summarized by means of analogical proportions, i.e., statements of the form “A is to B as C is to D”. Analogy is not a mere question of similarity between two objects (or situations), but rather a matter of proportion or relation between objects. This view dates back to Aristotle and was enforced by Scholastic philosophy. Indeed, an analogical proportion equates a relation between two objects with the relation between two other objects. As such, the analogical proportion “A is to B as C is to D” poses an analogy of proportionality by (implicitly) stating that the way the two objects A and B, otherwise similar, differ is the same way as the two objects C and D, which are similar in some respects, differ.
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  • HAL Id : hal-01154243, version 1
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Henri Prade, Gilles Richard. Homogenous and heterogeneous logical proportions. Journal of Logic and Computation, Oxford University Press (OUP), 2014, Vol. 1 (n° 1), pp. 1-52. ⟨hal-01154243⟩

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