有效消除Skolem函数 \(\text {LK}^\text {h}\)

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2021-11-22 DOI:10.1007/s00153-021-00798-z

Ján Komara

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引用次数: 0

摘要

我们提出了一个用Henkin常数代替自由变量的连续微积分。通过处理本征变量条件，我们得到了一个具有强局部性的证明系统——每个推理步骤的有效性只取决于其活动公式，而不取决于其上下文。我们的主要结果是：通过非Gentzen风格的算法在不诉诸正则化的情况下消除割，以及对于具有割的导数的子类，随着证明长度的线性增加消除Skolem函数。

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Efficient elimination of Skolem functions in \(\text {LK}^\text {h}\)

We present a sequent calculus with the Henkin constants in the place of the free variables. By disposing of the eigenvariable condition, we obtained a proof system with a strong locality property—the validity of each inference step depends only on its active formulas, not its context. Our major outcomes are: the cut elimination via a non-Gentzen-style algorithm without resorting to regularization and the elimination of Skolem functions with linear increase in the proof length for a subclass of derivations with cuts.

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.