弱可解释性逻辑上的持续性原则
The persistence principle over weak interpretability logic
AI总结：
本文研究在弱可解释性逻辑中加入持续性原则所得逻辑，证明其弱不动点性质、切消与 Craig 插值、有限标架性质及算术语义下的可靠完全性。
摘要：
我们关注弱可解释性逻辑上的持续性原则。研究对象是从若干视角出发，将持续性原则添加到弱可解释性逻辑中所得到的逻辑。首先，我们证明该逻辑具有弱版本的不动点性质。其次，我们引入一个矢列演算系统，并证明其切消定理。作为推论，我们证明该逻辑具有 Craig 插值性质。第三，我们表明该逻辑是简化 Veltman 语义的一种推广的自然基础，并证明它相对于该语义具有有限标架性质。最后，我们证明它相对于某种适当的算术语义是可靠且完全的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
