Modal Logic （Patrick & Blackburn）

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1、ModalLogicPatrickBlackburnpatrick@coli.uni-sb.deMaartendeRijkemdr@wins.uva.nlYdeVenemayde@wins.uva.nlForJohanContentsPrefacepageviii1BasicConcepts11.1RelationalStructures21.2ModalLanguages91.3ModelsandFrames161.4GeneralFrames271.5ModalConsequenceRelations311.

2、6NormalModalLogics331.7HistoricalOverview381.8SummaryofChapter1482Models502.1InvarianceResults512.2Bisimulations642.3FiniteModels732.4TheStandardTranslation832.5ModalSaturationviaUltrafilterExtensions912.6CharacterizationandDefinability1002.7SimulationandSafety

3、1102.8SummaryofChapter2118Notes1193Frames1243.1FrameDefinability1253.2FrameDefinabilityandSecond-OrderLogic1313.3DefinableandUndefinableProperties1393.4FiniteFrames1443.5AutomaticFirst-OrderCorrespondence1503.6SahlqvistFormulas1573.7MoreaboutSahlqvistFormulas168v

4、vi0Contents3.8AdvancedFrameTheory1803.9SummaryofChapter3185Notes1864Completeness1904.1Preliminaries1914.2CanonicalModels1984.3Applications2034.4LimitativeResults2134.5TransformingtheCanonicalModel2194.6Step-by-step2254.7RulesfortheUndefinable2314.8FinitaryMeth

5、odsI2414.9FinitaryMethodsII2484.10SummaryofChapter4258Notes2595AlgebrasandGeneralFrames2635.1LogicasAlgebra2645.2AlgebraizingModalLogic2765.3TheJ´onsson-TarskiTheorem2855.4DualityTheory2965.5GeneralFrames3055.6Persistence3195.7SummaryofChapter5327Notes3296Com

6、putabilityandComplexity3346.1ComputingSatisfiability3356.2DecidabilityviaFiniteModels3406.3DecidabilityviaInterpretations3496.4DecidabilityviaQuasi-modelsandMosaics3586.5UndecidabilityviaTiling3666.6NP3756.7PSPACE3836.8EXPTIME3956.9SummaryofChapter6407Notes408

7、7ExtendedModalLogic4157.1LogicalModalities4167.2SinceandUntil4287.3HybridLogic4367.4TheGuardedFragment448Contentsvii7.5Multi-DimensionalModalLogic4607.6ALindstr¨omTheoremforModalLogic4727.7SummaryofChapter7478Notes479AppendixAALogicalToolkit488AppendixBAnAlge

8、braicToolkit500AppendixCAComputationalToolkit507AppendixDAGuidetotheLiterature519Bibliography527Index547PrefaceAskthreemodallogicianswhatmodallogicis,andyouarelikelytogetatleastthreediffe