计算机科学 ›› 2023, Vol. 50 ›› Issue (6A): 220600013-5.doi: 10.11896/jsjkx.220600013

• 人工智能 • 上一篇    下一篇

命题逻辑中的L-型冗余性质

刘凌荣, 陈树伟, 姜世攀   

  1. 1 西南交通大学数学学院 成都 611756;
    2 系统可信性自动验证国家地方联合工程实验室 成都 611756
  • 出版日期:2023-06-10 发布日期:2023-06-12
  • 通讯作者: 陈树伟(swchen@swjtu.edu.cn)
  • 作者简介:(13509752194@163.com)
  • 基金资助:
    国家自然科学基金(61976130)

L-type Redundancy Property in Propositional Logic

LIU Lingrong, CHEN Shuwei, JIANG Shipan   

  1. 1 School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;
    2 National-Local Joint Engineering Laboratory of System Credibility Automatic Verification,Chengdu 611756,China
  • Online:2023-06-10 Published:2023-06-12
  • About author:LIU Lingrong,born in 1996,postgra-duate.His main research interests include automated reasoning and so on. CHEN Shuwei,born in 1977,Ph.D, as-sociate professor.His main research interests include logic based automated reasoning and decision analysis.
  • Supported by:
    National Natural Science Foundation of China(61976130).

摘要: 在命题逻辑SAT求解过程中,子句集简化技术是重要的一个环节。冗余性质所对应的子句消去方法可以准确识别并删除冗余子句。无论是在预处理阶段还是SAT求解过程中,子句消去方法嵌入到SAT求解器均可加快求解器的求解效率。现有的高效子句消去方法大多基于封锁子句冗余性质和蕴涵模归结子句冗余性质扩展而来,为检查子句C是否冗余,只需要考虑子句C是否满足冗余条件。提出一种L-型冗余性质,它是封锁冗余性质、包含冗余性质、蕴涵模归结冗余性质的推广,将冗余子句判断条件由单个文字的归结式拓展到文字集合的组合。然后,针对L-型冗余性质,分析L-型冗余子句具有的性质,并将L-型冗余子句与已有的冗余子句的高效性进行比较,说明所提出的L-型冗余性质的高效性。

关键词: 命题逻辑, 子句消去方法, L-型冗余性质

Abstract: The technique of clause set simplification is a crucial part in the process of propositional logic SAT solving.The clause elimination methods corresponding to the redundancy property can accurately identify and delete redundant clauses.Either in the pre-processing stage or in the process of SAT solving,the embedded clause elimination methods in the SAT solver accelerate the solving efficiency of the solver. A large number of efficient clause elimination methods are extended based on the redundancy properties of blocked clauses and implication module resolution clauses.In order to check whether clause C is redundant,we need only to consider whether clause C satisfies the redundancy conditions.The proposed L-type redundancy is an extension of the blocked redundancy property,subsumption redundancy property and implication module resolution redundancy. It extends the judgement condition of redundant clause from the resolution of single literal to the combination of the set of literals.According to the properties of L-type redundancy,this paper analyzes the properties of L-type redundancy clause,and applies comparison analy-sis on the efficiency of L-type redundancy clauses and other existed redundant clauses,so as to illustrate the efficiency of L-type redundancy clauses.

Key words: Propositional logic, Clause elimination method, L-type redundancy property

中图分类号: 

  • TP181
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