Computer Science > Artificial Intelligence
[Submitted on 7 Aug 2024]
Title:Frank's triangular norms in Piaget's logical proportions
View PDF HTML (experimental)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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