We introduce a novel, semantically inspired method of constructing nested sequent calculi for propositional intermediate logics. Applying recently developed methods for proving Craig interpolation to these nested sequent calculi, we obtain constructive proofs of the interpolation property for most non-trivial interpolable intermediate logics, as well as Lyndon interpolation for Gödel logic. Finally, we provide a prototype implementation combining proof search and countermodel construction.

中文翻译：

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通过内射嵌套序列对中间逻辑进行插值

我们介绍了一种新颖的、受语义启发的方法，用于为命题中间逻辑构建嵌套顺序演算。将最近开发的用于证明 Craig 插值的方法应用于这些嵌套的连续演算，我们获得了大多数非平凡可插值中间逻辑的插值属性的建设性证明，以及 Gödel 逻辑的林登插值。最后，我们提供了一个结合证明搜索和反模型构建的原型实现。