命题逻辑的子句集中文字的分类

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Title:

Classification of the characters in the set of clauses of propositional logic

作者:

邓鹏^1,2, 徐扬^1,2

1. 西南交通大学 数学学院, 四川 成都 611756;
2. 西南交通大学 智能控制开发中心, 四川 成都 610031

Author(s):

DENG Peng^1,2, XU Yang^1,2

1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China;
2. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China

关键词:

命题逻辑; 子句集; 冗余子句; 冗余文字; 可满足性

Keywords:

propositional logic; set of clauses; redundant clause; redundant character; satisfiability

分类号:

TH186

DOI:

10.11992/tis.201410005

文献标志码:

A

摘要:

检测和消除命题逻辑公式中的冗余文字,是人工智能领域广泛研究的基本问题。针对命题逻辑的子句集中子句的划分,结合冗余子句和冗余文字的概念,将命题逻辑的子句集中的文字分为必需文字、有用文字和无用文字3类,并分别给出其定义。讨论3种文字与无冗余等价子集的性质,给出其等价子集的等价描述方法。得到题逻辑的子句集中必需文字、有用文字和无用文字的判定方法,借助子句集的可满足性得到3种文字与子句集的可满足性的等价条件。上述结果对命题逻辑中文字属性的判断提供了多种可选择方法,同时为命题逻辑公式的化简奠定了理论基础。

Abstract:

The detection and elimination of redundant clauses from prepositional logic formulas is a fundamental issue that has been widely researched in artificial intelligence (AI). The concept for division in the set of clauses of propositional logic is combined with the concepts of redundant clause and redundant character so as to research the classification of the characters in the set of clauses of propositional logic. The characters are classified into three categories:necessary characters, useful characters, and useless characters, and thereby definitions of them are given, respectively. The property of three kinds of characters and irredundant equivalent subsets is discussed, some equivalent descriptions of these three kinds of characters and non-redundant equivalent subsets are given respectively. The judging method for these three kinds of characters in the set of clauses of propositional logic is obtained, and by virtue of the satisfiability of the set of clauses, the equivalent conditions of satisfiability for these three kinds of characters and the set of clauses are derived. These results provide a variety of alternative methods for judging the attributes of the characters of the set of clauses in propositional logic, laying a theoretical foundation for simplifying propositional logic formulas.