Non-Canonical Models of Relevant Logics

Abstract

We construct, in several ways, Fine-style frame models of the relevant logic $\textbf{B}$ which verify exactly the theorems of $\textbf{B}$ but differ from the canonical model in some of their properties: they contain multiple points representing the same (formal) $\textbf{B}$ theory, or their points fail to represent some formal $\textbf{B}$ theories (in fact, fail to represent almost all of them). We briefly discuss the implications of this for the adequacy of frame semantics for relevant logics.