A Novel View of Analogical Proportion Between Formulas Article Swipe
Andreas Herzig
,
Emiliano Lorini
,
Henri Prade
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3233/faia240624
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3233/faia240624
Analogical proportions are statements of the form “α is to β as γ is to δ”, noted α:β::γ:δ, and can be understood as “α differs from β as γ differs from δ” and conversely “β differs from α as δ differs from γ”. In this paper, α, β, γ, δ are supposed to be propositional logic formulas, which are appropriate for representing concepts. There exists one approach, developed over the last 15 years, where “α differs from β” is understood in terms of the negation of the material implication α → β. The paper investigates another view where “α differs from β” is interpreted in terms of transformations where some variables become false, some variables become true, and some variables become irrelevant. Both approaches satisfy the three basic postulates of analogical proportions (reflexivity, symmetry, and stability under central permutation), as well as other interesting properties such as transitivity and unicity of δ such that α:β::γ:δ. However, the two approaches depart from each other since they do not validate the same analogical proportions. In particular, when p,q,r are atoms the proportion p:(p∧r)::q:(q∧r) holds in the new approach, while it fails to do so for the other. The new approach exhibits also a good behaviour with respect to integrity constraints. It is advocated that this makes it appropriate for handling analogy between concepts, while the other approach has proved to be fruitful for Boolean features-based representations. The paper provides a thorough analysis of the differences between the two approaches.
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Metadata
- Type
- book-chapter
- Language
- en
- Landing Page
- https://doi.org/10.3233/faia240624
- https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA240624
- OA Status
- hybrid
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4403488030Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3233/faia240624Digital Object Identifier
- Title
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A Novel View of Analogical Proportion Between FormulasWork title
- Type
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book-chapterOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-10-16Full publication date if available
- Authors
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Andreas Herzig, Emiliano Lorini, Henri PradeList of authors in order
- Landing page
-
https://doi.org/10.3233/faia240624Publisher landing page
- PDF URL
-
https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA240624Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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hybridOpen access status per OpenAlex
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https://ebooks.iospress.nl/pdf/doi/10.3233/FAIA240624Direct OA link when available
- Concepts
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Analogy, Transitive relation, Negation, Analogical reasoning, Permutation (music), Propositional calculus, Mathematics, Algebra over a field, Pure mathematics, Epistemology, Computer science, Discrete mathematics, Combinatorics, Philosophy, Programming language, AestheticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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