Frank's triangular norms in Piaget's logical proportions
<|reference_start|>Frank's triangular norms in Piaget's logical proportions: 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.<|reference_end|>
@article{prade2024frank's,
    title={Frank's triangular norms in Piaget's logical proportions},
    author={Henri Prade and Gilles Richard},
    journal={arXiv preprint arXiv:2408.03795},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.03795},
    primaryClass={cs.AI}
}