Galois theory for analogical classifiers

Analogical proportions are 4-ary relations that read “A is to B as C is to D”. Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference. This inference mechanism was empirically proved to be efficient in several reasoning and cl...

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Bibliographic Details
Published inAnnals of mathematics and artificial intelligence Vol. 92; no. 1; pp. 29 - 47
Main Authors Couceiro, Miguel, Lehtonen, Erkko
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.01.2024
Springer Nature B.V
Springer Verlag
Subjects
Artificial Intelligence
Boolean
Classifiers
Cognition & reasoning
Complex Systems
Computer Science
Inference
Mathematics
Reflexivity
Analogical classifier
68T99
Analogical reasoning
06A15
Galois theory
Analogical proportion
analogical reasoning
analogical classifier
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Summary:Analogical proportions are 4-ary relations that read “A is to B as C is to D”. Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference. This inference mechanism was empirically proved to be efficient in several reasoning and classification tasks. In the latter case, it relies on the notion of analogy preservation. In this paper, we explore this relation between formal models of analogy and the corresponding classes of analogy preserving functions, and we establish a Galois theory of analogical classifiers. We illustrate the usefulness of this Galois framework over Boolean domains, and we explicitly determine the closed sets of analogical classifiers, i.e., classifiers that are compatible with the analogical inference, for each pair of Boolean analogies.
ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-023-09833-6