Analogical Proportions and Multiple-Valued Logics

Henri Prade (1, 2) , Gilles Richard (1)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique

Recently, a propositional logic modeling of analogical proportions, i.e., statements of the form “A is to B as C is to D”, has been proposed, and has then led to introduce new related proportions in a general setting. This framework is well-suited for analogical reasoning and classification tasks about situations described by means of Boolean properties. There is a clear need for extending this approach to deal with the cases where i) properties are gradual ; ii) properties may not apply to some situations ; iii) the truth status of a property is unknown. The paper investigates the appropriate extension in each of these three cases.

Mots clés: Analogical proportion; Multiple-valued logic; Three-valuedlogics

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Henri Prade, Gilles Richard. Analogical Proportions and Multiple-Valued Logics. 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2013), Jul 2013, Utrecht, Netherlands. pp. 497-509. ⟨hal-01197273⟩