含等词子句集上的子句冗余性原理

宁欣然; 吴贯锋; 徐扬

doi:10.3969/j.issn.0258-2724.20240586

含等词子句集上的子句冗余性原理

doi: 10.3969/j.issn.0258-2724.20240586

宁欣然^1,,
吴贯锋^2, ,,
徐扬²

1.
西南民族大学计算机与人工智能学院，四川成都 610225
2.
西南交通大学数学学院，四川成都 611752

基金项目: 国家自然科学基金项目（62106206）；中央高校基本科研业务费专项资金（ZYN2024054）

详细信息

作者简介:
宁欣然（1990—），女，讲师，博士，研究方向为自动推理，E-mail：ningxinran99@foxmail.com

通讯作者:
吴贯锋（1986—），男，工程师，博士，研究方向为自动推理、并行计算，E-mail： wgf1024@swjtu.edu.cn

中图分类号: TP391.1
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- 被引次数: 0
出版历程
- 收稿日期: 2024-11-12
- 修回日期: 2025-03-11
- 网络出版日期: 2025-12-19

Principle for Clause Redundancy in Clause Sets with Equality

NING Xinran^1
,,
WU Guanfeng^{2
, ,},
XU Yang²

1.
College of Computer Science and Artificial Intelligence, Southwest Minzu University, Chengdu 610225, China
2.
School of Mathematics, Southwest Jiaotong University, Chengdu 611752, China

摘要

摘要:
为探讨含等词子句集中的子句冗余性问题，提出一种新的子句冗余性判定方法——等词蕴涵模归结原理（EIMR）. 首先，分析一阶逻辑定理证明器在化简过程中对冗余子句的处理需求，指出蕴涵模归结原理无法直接应用于含等词子句集的不足；其次，通过结合平展操作与归结方法，定义适用于含等词子句集的等词蕴涵模归结原理，详细证明其理论可靠性，并阐明该原理在冗余子句判定中的具体作用；随后，以EIMR为基础，将命题逻辑和不含等词子句集上的子句消去方法扩展至含等词子句集，定义等词归结不对称恒真子句和等词归结包含子句，并证实这些扩展方法的有效性；最后，利用该原理进一步验证主流一阶逻辑定理证明器在预处理阶段中谓词消去方法的可靠性. 研究结果表明，等词蕴涵模归结原理为含等词子句集上的子句冗余性研究提供了理论依据，并扩展了现有子句消去方法的适用范围.
- 一阶逻辑定理证明 /
- 等词蕴涵模归结原理 /
- 子句冗余性 /
- 子句消去方法
Abstract:
To investigate clause redundancy in clause sets with equality, a determination method for clause redundancy, namely equality implication modulo resolution (EIMR) principle, was proposed. First, the need for handling redundant clauses during the simplification process in a first-order logic theorem prover was analyzed, and the limitations of implication modulo resolution principle in handling clause sets with equality were identified. By integrating flattening and resolution methods, the EIMR principle applicable to clause sets with equality was defined. The reliability of the principle was proven, and the specific role of the principle in the determination of redundant clauses was clarified. Subsequently, on the basis of EIMR, the clause elimination methods from propositional logic and clause sets without equality were extended to clause sets with equality. Asymmetric tautologies and subsumption clauses of equality resolution were defined, and the effectiveness of these methods was demonstrated. Finally, the reliability of predicate elimination preprocessing methods in mainstream first-order theorem provers was validated using the EIMR principle. The results indicate that EIMR provides a theoretical basis for clause redundancy studies in clause sets with equality and extends the applicable scope of existing clause elimination methods.
- first-order logic theorem proving /
- equality implication modulo resolution principle /
- clause redundancy /
- clause elimination method

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