Summary of Frank’s Triangular Norms in Piaget’s Logical Proportions, by Henri Prade and Gilles Richard
Frank’s triangular norms in Piaget’s logical proportions
by Henri Prade, Gilles Richard
First submitted to arxiv on: 7 Aug 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper proposes a definition of analogical proportion between numerical values using triangular norms and dual co-norms, building upon Piaget’s concept of logical proportion. The authors utilize Frank’s family of triangular norms to demonstrate the equivalence of Boolean notions with analogical proportions. The paper concludes by comparing its approach with another recent proposal based on generalized means. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This study helps us understand how we can compare numbers in a way that’s similar to how we think about things being “similar” or “alike”. It uses a mathematical concept called triangular norms, which is important for making comparisons between different types of data. The idea is to find a way to measure similarity between numbers, just like how we use language to describe similarities between concepts. |
