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Journal Articles Journal of Applied Logics - IfCoLoG Journal of Logics and their Applications Year : 2024

Analogical proportion-based induction: from classification to creativity

Abstract

The first aim of this article is to position analogical inference (or at least a particular form of it) in relation to induction. After a brief reminder on the induction of plausible conclusions in a probabilistic, logical, possibilistic settings, and with J. S. Mill’s methods of induction, we turn our attention to analogical inference, based on analogical proportions. Analogical proportions that hold between Boolean vectors are emphasized as a matter of pairs belonging to the same equivalence class. Then the mechanism of analogical proportions-based classification is explained and the main algorithms and results obtained so far are surveyed. After which, steps towards a logic of creativity are presented. The approach starts from the observation that analogical proportions belong to a larger set of quaternary relations called logical proportions. The six logical proportions giving birth to an equivalence relation between pairs are identified. This includes two important cases: i) a logic of conditional events known as being a basis for non monotonic reasoning (which is a form of plausible deduction) ; ii) a logic of ordered pairs preserving positive changes, closely related to analogical proportions. Within this framework, we revisit the creative nature of analogical proportions and introduce a creative inference mechanism that works on the basis of a specific situation and a collection of ordered pairs representing possible changes.
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Dates and versions

hal-04581067 , version 1 (21-05-2024)

Identifiers

  • HAL Id : hal-04581067 , version 1

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Henri Prade, Gilles Richard. Analogical proportion-based induction: from classification to creativity. Journal of Applied Logics - IfCoLoG Journal of Logics and their Applications, 2024, 11 (1), pp.51--87. ⟨hal-04581067⟩
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