Frank's triangular norms in Piaget's logical proportions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911980846055424 |
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| author | Prade, Henri Richard, Gilles |
| author_facet | Prade, Henri Richard, Gilles |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frank's triangular norms in Piaget's logical proportions Prade, Henri Richard, Gilles Artificial Intelligence 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. |
| title | Frank's triangular norms in Piaget's logical proportions |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2408.03795 |