Log 命题逻辑 基础部分: 逻辑( Logic) 集合(Sets) 算法( Algorithms 数论( Number Theory) 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 1 基础部分: 逻辑(Logic) 集合(Sets) 算法(Algorithms) 数论(Number Theory)
Log 命题逻辑 1.1逻辑 Logic 2/24/202111:14PM Deren Chen, ZheJiang Univ 2
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 2 1.1 逻辑 Logic
Log 命题逻辑 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 2/24/202111:14PM Deren Chen, ZheJiang Univ 3
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 3 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
Log 命题逻辑 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 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 4 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
Log 命题逻辑 命题逻辑 Proposition Logic 命题 Proposition: 个有确定真或假意义的语句. 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 5 命题 Proposition: 一个有确定真或假意义的语句. 命题逻辑 Proposition Logic
EXAMPLE1 命题逻辑 All the following statements are propositions. Washington, D.C. 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 I and 3 are true, whereas 2 and 4 are false 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 6 EXAMPLE1 All the following statements are propositions. 1. Washington, D.C., 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
EXAMPLE2 命题逻辑 Consider the following sentences. What time is it? 2. Read this carefully 3.X+1=2 4. x+y=Z Sentences I 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 1.3 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 7 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 1.3
Log 命题逻辑 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 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 8 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
Log 命题逻辑 命题的符号表示: 大小写英文字母:P、Q、R、 P、q 命题真值( TRuth values)的表示: 真:T、1 假:F 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 9 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
Log 命题逻辑 命题语句真值确定的几点说明: 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) 2/24/202111:14PM Deren Chen, ZheJiang Univ
L o g i c 命题逻辑 2/24/2021 11:14 PM Deren Chen, ZheJiang Univ. 10 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)
