直觉证明逻辑的解析演算

IF 0.6 3区数学 Q2 LOGIC

Notre Dame Journal of Formal Logic Pub Date : 2019-08-01 DOI:10.1215/00294527-2019-0008

Brian Hill, F. Poggiolesi

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引用次数: 1

摘要

本文的目标是朝着寻找证明逻辑的解析序列演算问题的解决迈出一步。为此，我们关注系统Ilp，证明逻辑的直觉主义版本。首先，我们给出了关于系统Ilp的完备的序贯演算;我们证明了Gilp是无切割和无收缩的，但它仍然不具有子公式性质。然后，我们丰富了证明逻辑的语言，并在这种语言中表述了第二个根岑微积分Gilp *。证明了Gilp∗是Gilp的保守扩展，并且Gilp∗满足子公式性质。关键词切消，证明逻辑，归一化，证明序列2010 MSC: 03F05, 03B60

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An Analytic Calculus for the Intuitionistic Logic of Proofs

The goal of this paper is to take a step towards the resolution of the problem of finding an analytic sequent calculus for the logic of proofs. For this, we focus on the system Ilp, the intuitionistic version of the logic of proofs. First we present the sequent calculus Gilp that is sound and complete with respect to the system Ilp; we prove that Gilp is cut-free and contraction-free, but it still does not enjoy the subformula property. Then, we enrich the language of the logic of proofs and we formulate in this language a second Gentzen calculus Gilp∗. We show that Gilp∗ is a conservative extension of Gilp, and that Gilp∗ satisfies the subformula property. Keyword cut-elimination, logic of proofs, normalisation, proof sequents 2010 MSC: 03F05, 03B60

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来源期刊

Notre Dame Journal of Formal Logic MATHEMATICS-LOGIC

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.