Characterization of Maximal Consistent Theories in Modal Logic S5

LI Bi-jing

doi:10.3969/j.issn.0372-2112.2014.08.014

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Characterization of Maximal Consistent Theories in Modal Logic S5

更新时间：2025-07-16

- Characterization of Maximal Consistent Theories in Modal Logic S5
- Acta Electronica Sinica Vol. 42, Issue 8, Pages: 1551-1555(2014)
- 作者机构：
  
  1. 宝鸡文理学院数学系,陕西,宝鸡,721013
  2. 宝鸡文理学院数学系,陕西,宝鸡,721013
- 作者简介：
- 基金信息：
  
  Youth Fund of National Natural Science Foundation of China (No.11001158);Key Research Program of Baoji University of Arts and Sciences (No.ZK1047)
- DOI：10.3969/j.issn.0372-2112.2014.08.014
  CLC： O141
- Published：2014
- 稿件说明：
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LI Bi-jing. Characterization of Maximal Consistent Theories in Modal Logic S5[J]. Acta Electronica Sinica, 2014, 42(8): 1551-1555.
DOI：

LI Bi-jing. Characterization of Maximal Consistent Theories in Modal Logic S5[J]. Acta Electronica Sinica, 2014, 42(8): 1551-1555. DOI： 10.3969/j.issn.0372-2112.2014.08.014.

摘要

在模态逻辑系统S5中提出了任意一模态公式关于一个极大相容理论的存在状态及状态描述等一系列概念，并且借助状态描述这一工具研究了相容理论的相容扩张，最后给出了模态逻辑系统S5中极大相容理论的一个结构刻画，证明了任何一个极大相容理论都是所有简单合取式和简单析取式的相容存在状态之集的理论闭包.

Abstract

The present paper proposes the definitions of state description and existing state for a formula with respect to a maximal consistent theory.Some important properties of consistent theory are obtained by using state description as the tool.Then

it is proved that maximal consistent theory is just the theoretical closure of consistent exist state of all simple disjunctive formulas and conjunctive ones.

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