A note on Kripke semantics for residuated logic

Residuated logic is a suitable logical system for approximate reasoning and for the development of fuzzy mathematics. Residuated propositional logic (RPC) is shown to be a fragment of a well-known substructural logic (denoted by HBCK). Using results for HBCK, Kriple-style semantics is described for RPC for which soundness and completeness theorems hold. These results answer a question previously posed for RPC and situate RPC in the currently active research field of substructural logics.