TitleOn a Three-Valued Logic to Reason with Prototypes and Counterexamples and a Similarity-Based Generalization
Publication TypeConference Paper
Year of Publication2016
AuthorsSoma D, Esteva F, Godo L
Conference NameCAEPIA 2016

In this paper, the meaning of a vague concept ? is assumed to be rendered through two (mutually exclusive) finite sets of prototypes and counterexamples. In the remaining set of situations the concept is assumed to be applied only partially. A logical model for this setting can be fit in to the three-valued Lukasiewicz’s logic L_3 set up by considering, besides the usual notion of logical consequence |= (based on the truth preservation), the logical consequence |=? based on the preservation of all truth-degrees as well. Moreover, we go one step further by considering a relaxed notion of consequence to some degree a ? [0, 1], by allowing the prototypes (counterexamples) of the premise (conclusion) be a-similar to the prototypes (counterexamples) of the conclusion (premise). We present a semantical characterization as well as an axiomatization.