Non-Commutative Fuzzy Logics and Substructural Logics

摘要

This report treats the relation between substructural logics and fuzzy logics, especially focuses on the non-commutativity of conjunctive operators i.e. substructural logics without the exchange rule. As the results, the authors show that fuzzy logics based on the left continuous pseudo-t-norms form the models of FL_W. Also, we introduce the definition of pseudo-uninorms and give some methods to construct them, and show that such functions realize the fuzzy logical systems as the models of FL_c and FL, which is the weakest substructural logic.