Analogical proportions and multiple-valued logics

Authors:
Henri Prade;Gilles Richard
Affiliations:
IRIT, University of Toulouse, Toulouse, France;IRIT, University of Toulouse, Toulouse, France
Venue:
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2013

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Abstract

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.