A Similarity-Based Three-Valued Modal Logic Approach to Reason with Prototypes and Counterexamples

In this paper we focus on the application of similarity relations to formalise different kinds of graded approximate reasoning with gradual concepts. In particular we extend a previous approach that studies properties of a kind of approximate consequence relations for gradual propositions based on the similarity between both prototypes and counterexamples of the antecedent and the consequent. Here we define a graded modal extension of Łukasiewicz’s three-valued logic Ł3 and we show how the above mentioned approximate consequences can be interpreted in this modal framework, while preserving both prototypes and counterexamples.

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