Craig’s interpolation theorem has numerous applications in model checking, automated reasoning, and synthesis. There is a variety of interpolation systems which derive interpolants from refutation proofs; these systems are ad-hoc and rigid in the sense that they provide exactly one interpolant for a given proof. In previous work, we introduced a parametrised interpolation system which subsumes existing interpolation methods for propositional resolution proofs and enables the systematic variation of the logical strength and the elimination of non-essential variables in interpolants. In this paper, we generalise this system to propositional hyper-resolution proofs as well as clausal proofs. The latter are generated by contemporary SAT solvers. Finally, we show that, when applied to local (or split) proofs, our extension generalises two existing interpolation systems for first-order logic and relates them in logical strength.

中文翻译：

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用于超分辨率、子句和局部证明的标记插值系统

Craig 的插值定理在模型检查、自动推理和综合方面有很多应用。有多种插值系统可以从反驳证明中导出插值；这些系统是临时的和严格的，因为它们为给定的证明提供了一个插值。在之前的工作中，我们引入了一个参数化插值系统，该系统包含用于命题解析证明的现有插值方法，并能够系统地改变逻辑强度并消除插值中的非本质变量。在本文中，我们将该系统推广到命题超分辨率证明以及从句证明。后者由当代 SAT 求解器生成。最后，我们表明，当应用于局部（或分割）证明时，