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Frank's triangular norms in Piaget's logical proportions

Artificial Intelligence 2024-08-08 v1

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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Cite

@article{arxiv.2408.03795,
  title  = {Frank's triangular norms in Piaget's logical proportions},
  author = {Henri Prade and Gilles Richard},
  journal= {arXiv preprint arXiv:2408.03795},
  year   = {2024}
}

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6 pages