摘要
Interpretability logic is a modal formalization of relative interpretability between first-order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w-bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge models.
摘要译文
可解释性逻辑是一阶算术理论之间相对可解释性的模态形式化。Verbrugge语义是对Veltman语义的概括，这是解释性逻辑的基本语义。仿真是模态逻辑模型之间的基本等效性。我们研究了Verbrugge模型之间的各种双分裂概念，并开发了一种新的概念，我们称之为W-构图。我们表明，新的概念在保持双比喻意味着模态等价性的基本属性的同时，足够弱，可以使匡威在限制案例中保持。为此，我们在Verbrugge模型之间开发并使用了适当的分组游戏概念。
Sebastijan Horvat[1];Tin Perkov[2];Mladen Vuković[1]. Bisimulations and bisimulation games between Verbrugge models[J]. Mathematical Logic Quarterly, 2023,69(2): 231-243