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1、ANewApproachtoQuantumLogicK.EngesserKurt.Engesser@uni-konstanz.deD.M.Gabbaydov.gabbay@kcl.ac.ukD.Lehmannlehmann@cs.huji.ac.il2Contents1Introduction72ACrashCourseinLogic112.1BasicsofClassicalPropositionalLogic...............112.1.1IntroductoryRemarks.......
2、.............122.1.2SyntaxofClassicalPropositionalLogic..........132.1.3AHilbertstyledeductivesystemforclassicalproposi-tionallogic..........................142.1.4SemanticsofClassicalPropositionalLogic.........192.1.5SoundnessandCompleteness..............
3、..192.1.6Compactness.........................202.1.7Lattices............................212.1.8TheLindenbaumalgebra..................222.2BasicsofNonmonotonicLogic....................242.2.1Whatisnonmonotoniclogic?................242.2.2Non-monotonicityinq
4、uantummechanics.........252.2.3Inferenceoperationsandconsequencerelations......262.2.4TheconceptofaGKLMmodel...............263SomeHilbertSpaceTheory293.1TheConceptofaHilbertSpace...................293.2ClosedsubspacesandprojectionsinHilbertspace.........31
5、3.3OrthonormalsystemsandtheFourierexpansion.........323.4MoreLatticeTheory.........................353.5Thelatticeofclosedsubspacesandprojectionsofanorthomod-ularspace...............................383.6CharacterisingclassicalHilbertlattices...............
6、404BasicsoftheFormalismofQuantumMechanics434.1SomeHistory.............................434.2Hermitianoperators.........................454.3PostulatesofQuantumMechanics.................4634CONTENTS5Birkho?-vonNeumann1936495.0.1Structureofthepaper...........
7、.........505.0.2Novellogicalnotionsinquantummechanics........505.0.3ExperimentalPropositions..................525.0.4Apropositionalcalculusforquantummechanics.....535.0.5ThecorrespondencebetweenBirkho?andvonNeumannnduringthewritingofthepaper...............
8、585.0.6TheKochen-SpeckerandtheSch?utteTautologies.....606TheDynamicViewpoint:PropositionsasOperators616.1Propositionsvieweddynamically..................616.2TheConceptofanM-Algebra....................626.3Mot
