A Natural Proof System for Herbrand's Theorem
A Natural Proof System for Herbrand's Theorem
复制标题
赫布兰德定理的自然证明系统
DOI：
10.1007/978-3-319-72056-2_18
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Ralph
中科院分区：
文献类型：
--
作者：
B. Ralph
通过赫布兰德定理将不可判定的一阶逻辑还原为可判定的命题逻辑长期以来一直是理论计算机科学的兴趣，赫布兰德证明的概念激发了扩展证明的定义。围绕扩展证明构建自然证明系统的问题，具有证明的组合和无割完整性，已经从各种不同的角度进行了解决。在本文中，我们基于扩展证明的概念构建了一个简单的一阶逻辑深度推理系统，在新窗口中打开图像，作为围绕此基础发展丰富的证明理论的起点。给出了该系统中的证明和扩展证明之间的翻译，保留了每个方向的大部分结构。
The reduction of undecidable first-order logic to decidable propositional logic via Herbrand’s theorem has long been of interest to theoretical computer science, with the notion of a Herbrand proof motivating the definition of expansion proofs. The problem of building a natural proof system around expansion proofs, with composition of proofs and cut-free completeness, has been approached from a variety of different angles. In this paper we construct a simple deep inference system for first-order logic, Open image in new window , based around the notion of expansion proofs, as a starting point to developing a rich proof theory around this foundation. Translations between proofs in this system and expansion proofs are given, retaining much of the structure in each direction.
经典林业证明
影响因子：
0.8
作者：
Heijltjes W
通讯作者：
Heijltjes W