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(Involutive) Basic Substructural Fuzzy Logics and Urquhart-style Semantics
Eunsuk Yang
This paper addresses operational Kripke-style semantics for basic fuzzy substructural logics and their involutive extensions. First, we discuss fuzzy logic based on mianorm and their algebraic semantics together with their algebraic completeness. We next introduce various sorts of binary operational Kripke-style semantics, called here Urquhart-style semantics, for the systems and establish soundness and completeness results for them. In particular, we establish two kinds of completeness results, which we shall call algebra-based and set-theoretic completeness. Finally, we extend this investigation to involutive fuzzy logics and their corresponding Urquhart-style semantics.
Keywords: (core) fuzzy logics, algebraic semantics, Kripke-style semantics, involution, Urquhart-style semantics