命题逻辑proposition logic

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1、基础部分:逻辑(Logic)集合(Sets)算法(Algorithms)数论(NumberTheory)8/15/20211DerenChen,ZheJiangUniv.1.1逻辑Logic8/15/20212DerenChen,ZheJiangUniv.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8/15/20213DerenChen,ZheJiangUniv.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8/15/20214DerenChen

2、,ZheJiangUniv.命题Proposition:一个有确定真或假意义的语句.命题逻辑PropositionLogic8/15/20215DerenChen,ZheJiangUniv.EXAMPLE1Allthefollowingstatementsarepropositions.1.Washington,D.C.,isthecapitaloftheUnitedStatesofAmerica.2.TorontoisthecapitalofCanada.3.1+1=2.4.2+2=3.Propositions1and3aretrue,whereas2an

3、d4arefalse.8/15/20216DerenChen,ZheJiangUniv.EXAMPLE2Considerthefollowingsentences.1.Whattimeisit?2.Readthiscarefully.3.x+1=2.4.x+y=z.Sentences1and2arenotpropositionsbecausetheyarenotstatements.Sentences3and4arenotpropositionsbecausetheyareneithertruenorfalse,sincethevariablesinthes

4、esentenceshavenotbeenassignedvalues.VariouswaystoformpropositionsfromsentencesofthistypewillbediscussedinSection1.3.8/15/20217DerenChen,ZheJiangUniv.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8/15/20218DerenChen,ZheJiangUniv.命题的符号表示：大小写英文字母：P、Q、R、p、q、r、命题真值（TruthValues）的表示：真：T、1假：F、08/15/

5、20219DerenChen,ZheJiangUniv.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（TruthTable)8/15/202110DerenChen,ZheJiangUniv.DEFINITION1.Letpbeaproposition.Thestatement"Itisnotthecasethatp."isanotherproposition,calledthenegationofp.Thenegationofpisdenotedbyp.Thepropositionpisread"notp."p的否

6、定8/15/202111DerenChen,ZheJiangUniv.EXAMPLE3Findthenegationoftheproposition"TodayisFriday"andexpressthisinsimpleEnglish.Thenegationis"ItisnotthecasethattodayisFriday."Thisnegationcanbemoresimplyexpressedby''TodayisnotFriday."8/15/202112DerenChen,ZheJiangUniv.Table18/15/202113DerenCh

7、en,ZheJiangUniv.DEFINITION2.Letpandqbepropositions.Theproposition"pandq,"denotedbyp∧q,isthepropositionthatistruewhenbothpandqaretrueandisfalseotherwise.Thepropositionp∧qiscalledtheconjunctionofpandq.Thetruthtableforp∧qisshowninTable2.p和q的合取8/15/202114DerenChen,ZheJiangUniv.Table28/

8、15/202115DerenChen,ZheJian