The provability logic of a theory T captures the structural behavior of formalized provability in T as provable in T itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability logics. Where provability logics are the same for all moderately sound theories of some minimal strength, interpretability logics do show variations.The logic IL (All) is defined as the collection of modal principles that are provable in any moderately sound theory of some minimal strength. In this article we raise the previously known lower bound of IL (All) by exhibiting two series of principles which are shown to be provable in any such theory. Moreover, we compute the collection of frame conditions for both series.

中文翻译：

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所有合理算术理论的可解释性逻辑中的两个新原理系列

理论的可证明性逻辑吨捕捉形式化可证明性的结构行为吨如可证明的那样吨本身。与可证明性一样，人们可以将相对可解释性的概念形式化，从而产生可解释性逻辑。在可证明性逻辑对于所有具有某种最小强度的适度合理的理论来说是相同的情况下，可解释性逻辑确实显示出变化。逻辑伊利诺伊州(All) 被定义为模态原理的集合，这些模态原理可以在任何具有某种最小强度的适度合理的理论中得到证明。在本文中，我们提出了先前已知的下界伊利诺伊州（全部）通过展示在任何此类理论中被证明是可证明的两个系列的原理。此外，我们计算了两个系列的帧条件集合。