Topological semantics of conservativity and interpretability logics. (30th July 2021)

• Record Type: Journal Article
• Authors: Iwata, Sohei; Kurahashi, Taishi
• Is Part Of: Journal of logic and computation. Volume 31:Number 7(2021)
• Page Start: 1716
• Page End: 1739
• Publication Date: 2021-07-30
• Subjects: Provability logic -- conservativity logic -- interpretability logic -- strong completeness -- topological semantics; Logic programming -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; Computational complexity -- Periodicals; 005.115
• DOI: 10.1093/logcom/exab046
• Languages: English
• ISSNs: 0955-792X

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.