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Substructural Fuzzy-relevance Logic
October 21, 2015 @ 10:00 am
This talk proposes a new topic in substructural logic joining the fields of relevance and fuzzy logics. We first introduce fuzzy systems satisfying an old relevance principle, i.e., Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm (based) systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication (without distributivity) and its neighbors. The algebraic structures corresponding to the systems are then defined, and completeness results are provided. We next consider fuzzy systems satisfying new relevance principles introduced by Yang. We show that the weakening-free uninorm (based) systems and some extensions and neighbors of R satisfy the new relevance principles.