Residuated Basic Logic II. Interpolation, Decidability and Embedding

Abstract

We prove that the sequent calculus $\mathsf{L_{RBL}}$ for residuated basic logic $\mathsf{RBL}$ has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic $\mathsf{BPL}$. Thus $\mathsf{RBL}$ is decidable. Moreover, it follows that the class of residuated basic algebras has the finite embeddability property, and that $\mathsf{BPL}$ is PSPACE-complete, and that intuitionistic logic can be embedded into the modal logic $\mathsf{K4}$.