Topological semantics of conservativity and interpretability logics
| Autor: | Sohei Iwata, Taishi Kurahashi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Logic 010102 general mathematics Mathematics - Logic 0102 computer and information sciences Topological semantics 01 natural sciences Theoretical Computer Science Arts and Humanities (miscellaneous) Construction method 010201 computation theory & mathematics Hardware and Architecture Compactness theorem FOS: Mathematics 0101 mathematics Logic (math.LO) Software Mathematics Interpretability |
| DOI: | 10.48550/arxiv.2102.02483 |
| Popis: | 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. Comment: 28 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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