信息与计算科学毕业设计.doc

安徽建筑工业学院
毕业设计(论文)
专业信息与计算科学
班级 07信息(2)班
学生姓名汪保来
学号 07207010214
课题不同逻辑间翻译的完备性
指导教师王焕宝
2011年5月31日
不同逻辑间翻译的完备性
汪保来
(安徽建筑工业学院数理系,合肥230022)
摘要: 、计算机科学、人工智能、语言学等学科均有密切的联系,,而各门学科只研究自身的具体规律.
本论文讨论了在论域有限的情况下,,,二阶逻辑到一阶逻辑的翻译是满足完备性的.
关键字: 完备性;语义忠实翻译;语义满翻译;二阶逻辑;一阶逻辑
pleteness on translation
between different logical
Abstract Mathematical logic is to use mathematical methods to study the structure and reasoning in the form of the law of mathematics reasoning. It with other branches of mathematics, computer science, artificial intelligence, linguistics and other subjects are closely linked, It is increasingly shows its important role and a more broad application prospects. Mathematical Logic is the product of bination of Formal Logic and mathematical thinking, but mathematical logic is the study of various disciplines together ply with the general laws of logic, but All subjects only research their own specific rules.
The situation of this paper discusses the domain limited , the relationship between Propositional logic and first-order logic. In this paper, two logic properties: the failthfulness and the fullness are defined to ensure the preservations of the satisfiability and the unsatisfiability. In this paper, translation between Second-order logic and first-order logic pleteness in Henkin semantics.
Key pleteness; faithful translation; full translation; second-order logic; first-order
目录
摘要 II
ABSTRACT III
第一章绪论 1
1
主要问题及研究意义 1
第二章命题逻辑与一阶逻辑 3
3
4
一阶逻辑基本概念 4
5
5
6
6
6
6
7
第三章二阶逻辑 9
二阶逻辑的简介 9
11
性质的介绍及证明 11
完备性定理 12
二阶逻辑到一阶逻辑翻译的完备性的分析 17
第四章总结与展望 18
总