Topological semantics of conservativity and interpretability logics

Abstract

Abstract We introduce and develop a topological semantics of conservativity logics and interpretability logics. We prove the topological compactness theorem of consistent normal extensions of the conservativity logic $\textbf {CL}$ by extending Shehtman’s ultrabouquet construction method to our framework. As a consequence, we prove that several extensions of $\textbf {CL}$ such as $\textbf {IL}$, $\textbf {ILM}$, $\textbf {ILP}$ and $\textbf {ILW}$ are strongly complete with respect to our topological semantics.