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arXiv · 2102.02483

Topological semantics of conservativity and interpretability logics

Sohei Iwata·Taishi Kurahashi
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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 $\mathbf{CL}$ by extending Shehtman's ultrabouquet construction method to our framework. As a consequence, we prove that several extensions of $\mathbf{CL}$ such as $\mathbf{IL}$, $\mathbf{ILM}$, $\mathbf{ILP}$ and $\mathbf{ILW}$ are strongly complete with respect to our topological semantics.

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Sohei Iwata, Taishi Kurahashi. 2021-02-04. Topological semantics of conservativity and interpretability logics. https://doi.org/10.1093/logcom%2Fexab046

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