The persistence principle over weak interpretability logic

Pub Date : 2023-10-27 DOI:10.1002/malq.202200020
Sohei Iwata, Taishi Kurahashi, Yuya Okawa
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Abstract

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.

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弱可解释性逻辑的持久性原则
我们重点研究弱可解释性逻辑的持久性原理。我们的研究对象是在弱可解释性逻辑中加入持久性原理后得到的逻辑。首先,我们证明该逻辑具有弱版本的定点属性。其次,我们引入了一个序列微积分系统,并证明了它的切分消除定理。因此,我们证明该逻辑具有克雷格插值属性。第三,我们证明了该逻辑是简化维尔特曼语义学一般化的自然基础,并证明它具有与该语义学相关的有限框架属性。最后,我们证明,就某些适当的算术语义而言,它是健全和完整的。
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