Michal Walicki - 2006 - Introduction to Logic

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1、MMA)B_8x9y:(P(x)!Q(x;y)^R(y))Mj=A_Mj=vB,[A]=1_[B]v=1;9M:hfq0;q1g;f0;1g;q0;i`S0;`NB!B;8x:x=x_?IntroductiontoLogicMichalWalicki2006MMA)B_8x9y:(P(x)!Q(x;y)^R(y))Mj=A_Mj=vB,[A]=1_[B]v=1;9M:hfq0;q1g;f0;1g;q0;i`S0;`NB!B;8x:x=x_?iiContentsTheHistoryofLogic

2、1ALogic{patternsofreasoning1A.1Reductioadabsurdum..................................1A.2Aristotle..........................................2A.3Otherpatternsandlaterdevelopments.........................4BLogic{alanguageaboutsomething5B.1Earlysemanticobser

3、vationsandproblems.......................5B.2TheScholastictheoryofsupposition...........................6B.3Intensionvs.extension..................................6B.4Modalities.........................................7CLogic{asymboliclanguage7C.1Theun

4、iversallycharacteristiclanguage"........................8D19thand20thCentury{mathematizationoflogic9D.1GeorgeBoole........................................10D.2GottlobFrege.......................................12D.3Settheory.............................

5、............14D.420thcenturylogic.....................................15EModernSymbolicLogic16E.1Formallogicalsystems:syntax...............................16E.2Formalsemantics.....................................19E.3ComputabilityandDecidability........

6、.....................21FSummary23Bibliography23PartI.BasicSetTheory281.Sets,Functions,Relations281.1.SetsandFunctions....................................281.2.Relations..........................................321.3.OrderingRelations....................

7、................331.4.Innities..........................................352.Induction422.1.Well-FoundedOrderings.................................422.1.1.InductiveProofsonWell-foundedOrderings..................432.2.InductiveDenitions..................

8、.................472.2.1.1-1"Denitions..................................492.2.2.InductiveDenitionsandRecursiveProgramming...............502.2.3.ProofsbyStructuralInduction..........................532.3.TransniteInduction[opt