论文标题
新常态：我们无法消除co诱导的划线，但我们可以探索它们
The New Normal: We Cannot Eliminate Cuts in Coinductive Calculi, But We Can Explore Them
论文作者
论文摘要
在依次的计算中，削减消除是一种保证可以通过分析证明任何可证明的公式的属性。例如，Engzen的古典和直觉的计算LK和LJ享受削减的消除。该特性在序列钙化的共同诱导延伸中进行了较少的研究。在本文中，我们使用共同感应的角条款理论来表明在LJ的共同传感扩展中，剪切是我们称为CLJ的系统。我们从这项研究中得出了两个实际结果。我们证明了Gupta等人的Colp。用FixPoint项引起CLJ中的无剪切证明，我们制定并实施了一种新颖的共同诱导理论探索方法，该方法为CLJ中的剪切公式提供了几种启发式方法。
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. In this paper, we use coinductive Horn clause theories to show that cut is not eliminable in a coinductive extension of LJ, a system we call CLJ. We derive two further practical results from this study. We show that CoLP by Gupta et al. gives rise to cut-free proofs in CLJ with fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics for discovery of cut formulae in CLJ.
