Frank's triangular norms in Piaget's logical proportions

Henri Prade; Gilles Richard

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arXiv · 2408.03795

Frank's triangular norms in Piaget's logical proportions

Henri Prade·Gilles Richard

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Abstract

Starting from the Boolean notion of logical proportion in Piaget's sense, which turns out to be equivalent to analogical proportion, this note proposes a definition of analogical proportion between numerical values based on triangular norms (and dual co-norms). Frank's family of triangular norms is particularly interesting from this perspective. The article concludes with a comparative discussion with another very recent proposal for defining analogical proportions between numerical values based on the family of generalized means.

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Henri Prade, Gilles Richard. 2024-08-07. Frank's triangular norms in Piaget's logical proportions. https://arxiv.org/abs/2408.03795

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