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イワタ ソウヘイ
IWATA Sohei
岩田 荘平 所属 教養部 教養部本属 職種 講師 |
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| 言語種別 | 英語 |
| 発行・発表の年月 | 2023/10/27 |
| 形態種別 | 学術雑誌 |
| 査読 | 査読あり |
| 標題 | The persistence principle over weak interpretability logic |
| 執筆形態 | 共著 |
| 掲載誌名 | Mathematical Logic Quarterly |
| 掲載区分 | 国外 |
| 総ページ数 | 27 |
| 担当範囲 | Section 3 |
| 著者・共著者 | Taishi Kurahashi, Yuya Okawa |
| 概要 | We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this logic enjoys a weak version of the fixed point property. Secondly, we introduce a system of sequent calculus and prove the cut-elimination theorem for it. As a consequence, we prove that the logic enjoys the Craig interpolation property. Thirdly, we show that the logic is the natural basis of a generalization of simplified Veltman semantics, and prove that it has the finite frame property with respect to that semantics. Finally, we prove that it is sound and complete with respect to some appropriate arithmetical semantics. |