This paper deals with non-algebraic binary relational semantics, called here set-theoretic Kripke-style semantics, for monoidal t-norm (based) logics. For this, we first introduce the system MTL (Monoidal t-norm logic) and some of its prominent axiomatic extensions, and then their corresponding Kripke-style semantics. Next, we provide set-theoretic completeness results for them.
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