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Title:
命题模态逻辑的模型构造和完备性证明
Alternative Title: MODEL CONSTRUCTION AND COMPLETENESS PROOF OF PROPOSITIONAL MODAL LOGIC
Author: 柳欣欣 ; 李小燕
Keyword: Fisher-Ladner闭包 ; canonical model ; R规则 ; 可满足性 ; 完备性 ; Fisher-Ladner closure ; Canonical model ; R-rule ; Satisfiability ; Completeness
Source: 计算机应用与软件
Issued Date: 2014
Volume: 31, Issue:8, Pages:9-12,24
Indexed Type: CSCD
Department: 中国科学院软件研究所计算机科学国家重点实验室 北京100190 中国科学院软件研究所计算机科学国家重点实验室 北京100190 ;中国科学院研究生院 北京100190 ;中国科学院大学 北京 100190
Abstract: 模态逻辑是研究必然、可能及其相关概念的逻辑.模态公式的可满足性问题和证明系统的完备性问题是模态逻辑中的两个经典的问题.为了解决这两个问题,提出一个构造模态公式的canonical model的方法.通过这个方法,对于给定模态公式(φ),如果(φ)是可满足的,可以得到(φ)的一个canonical model;如果(φ)是不可满足的,可以得到(Γ)(φ)的证明.此外,还给出命题模态逻辑完备性的一个构造性证明方法.
English Abstract: Propositional modal logic is the logic studying the necessity,possibility and their correlated concepts. The satisfiability problem of model formula and the proof of system completeness problem are two classic problems in modal logic. To solve these two problems, we propose a method of canonical model to construct the modal formula. By this method,for a given model formula phi, if phi is satisfiable,a canonical model can be obtained for it ; but if phi is not satisfiable,a proof of its negation- phi is to be obtained. In addition,in the paper we also give a constructive proof method of the completeness of the propositional modal logic.
Language: 中文
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16717
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
柳欣欣,李小燕. 命题模态逻辑的模型构造和完备性证明[J]. 计算机应用与软件,2014-01-01,31(8):9-12,24.
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