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首页> 外文期刊>Journal of logic and computation >From the subformula property to cut-admissibility in propositional sequent calculi
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From the subformula property to cut-admissibility in propositional sequent calculi

机译：从子式性质到命题继发结石的切入性

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摘要

While the subformula property is usually a trivial consequence of cut-admissibility in sequent calculi, it is unclear in which cases the subformula property implies cut-admissibility. In this paper, we identify two wide families of propositional sequent calculi for which this is the case: the (generalized) subformula property is equivalent to cut-admissibility. For this purpose, we employ a semantic criterion for cut-admissibility, which allows us to uniformly handle a wide variety of calculi. Our results shed light on the relation between these two fundamental properties of sequent calculi and can be useful to simplify cut-admissibility proofs in various calculi for non-classical logics, where the subformula property (equivalently, the property known as 'analytic cut-admissibility') is easier to show than cut-admissibility.(1)
机译：虽然子公式属性通常是继发结石中切口可允许性的琐碎结果，但尚不清楚在哪种情况下，子公式属性暗示切口可允许性。在本文中，我们确定了以下两个大类命题后继结石：（广义）子公式属性等同于可采性。为此，我们采用了切入允许性的语义标准，这使我们能够统一处理各种各样的结石。我们的结果阐明了继发结石的这两个基本属性之间的关系，并且对于简化非经典逻辑的各种计算中的可割性可取性证明很有用，其中子公式属性（等效地，称为“解析可割性” '）比允许切入更容易显示。（1）

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