Handling analogical proportions in classical logic and fuzzy logics settings

Laurent Miclet (1) , Henri Prade (2)

1 IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

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.

Domaines: Intelligence artificielle [cs.AI]

Laurent Miclet, Henri Prade. Handling analogical proportions in classical logic and fuzzy logics settings. 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009), Jul 2009, Verona, Italy. pp.638-650, ⟨10.1007/978-3-642-02906-6_55⟩. ⟨hal-03353609⟩