1.1---逻辑.ppt

1.1---逻辑.ppt基础部分:
逻辑(Logic)
集合(Sets)
算法(Algorithms)
数论(Number Theory)
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Deren Chen, ZheJiang Univ.
逻辑
Logic
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Deren Chen, ZheJiang Univ.
逻辑学:
研究推理的一门学科
数理逻辑:
用数学方法研究推理的一门数学学科
-------- 一套符号体系+ 一组规则
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Deren Chen, ZheJiang Univ.
数理逻辑的内容:
古典数理逻辑:
命题逻辑、谓词逻辑
现代数理逻辑:
公理化集合论、递归论、模型论、证明论
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Deren Chen, ZheJiang Univ.
命题 Proposition:
一个有确定真或假意义的语句.
命题逻辑
Proposition Logic
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Deren Chen, ZheJiang Univ.
EXAMPLE 1
All the following statements are propositions.
1. Washington, ., is the capital of the United States of America.
2. Toronto is the capital of Canada.
3. 1+1=2.
4. 2+2=3.
Propositions 1 and 3 are true, whereas 2 and 4 are false.
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Deren Chen, ZheJiang Univ.
EXAMPLE 2
Consider the following sentences.
1. What time is it?
2. Read this carefully.
3. x+1 =2.
4. x+y = z.
Sentences 1 and 2 are not propositions because they are not statements. Sentences 3 and 4 are not propositions because they are neither true nor false, since the variables in these sentences have not been assigned values. Various ways to form propositions from sentences of this type will be discussed in Section .
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Deren Chen, ZheJiang Univ.
命题的语句形式
陈述句
非命题语句:
疑问句
命令句
感态句
非命题陈述句:悖论语句
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Deren Chen, ZheJiang Univ.
命题的符号表示:
大小写英文字母:P、Q、R、
p 、q 、r、
命题真值(Truth Values)的表示:
真:T、1
假:F、0
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Deren Chen, ZheJiang Univ.
命题语句真值确定的几点说明:
1、时间性
2、区域性
3、标准性
命题真值间的关系表示:
真值表(Truth Table)
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Deren Chen, ZheJiang Univ.