Handling Analogical Proportions in Classical Logic and Fuzzy Logics Settings

Analogical proportions are statements of the form "A is to B as C is to D" which play a key role in analogical reasoning. We propose a logical encoding of analogical proportions in a propositional setting, which is then extended to different fuzzy logics. Being in an analogical proportion is viewed as a quaternary connective relating four propositional variables. Interestingly enough, the fuzzy formalizations that are thus obtained parallel numerical models of analogical proportions. Potential applications to case-based reasoning and learning are outlined.

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