论文标题
关于弱解释性逻辑的持久原则
The persistence principle over weak interpretability logic
论文作者
论文摘要
我们专注于弱势可解释性逻辑的持久性原则。我们的研究对象是通过从几个角度将持久性原理添加到弱的可解释性逻辑中获得的逻辑。首先，我们证明了这种逻辑具有不可测的固定点属性。其次，我们引入了一个顺序的微积分系统，并证明了它的切割定理。结果，我们证明逻辑享有Craig插值属性。第三，我们表明逻辑是简化Veltman语义的概括的自然基础，并证明它具有相对于该语义的有限框架属性。最后，我们证明，相对于某些适当的算术语义，它是合理的和完整的。
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.
