A Logical Theory of Causality

367 Pages·2021·2.767 MB·English

by  Alexander Bochman

ALogicalTheoryofCausality

ALogicalTheoryofCausality
AlexanderBochman
TheMITPress
Cambridge,Massachusetts
London,England
© 2021 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic or
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The MIT Press would like to thank the anonymous peer reviewers who provided comments on
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This book was set in Times Roman by Alexander Bochman.
Library of Congress Cataloging-in-Publication Data
Names: Bochman, Alexander, 1955 author.
Title: A logical theory of causality / Alexander Bochman.
Description: Cambridge, Massachusetts : The MIT Press, 2021. | Includes bibliographical
references and index.
Identifiers: LCCN 2020037281 | ISBN 9780262045322 (paperback)
Subjects: LCSH: Nonmonotonic reasoning. | Causation. | Logistics.
Classification: LCC Q339.2 .B628 2021 | DDC 122–dc23
LC record available at https://lccn.loc.gov/2020037281
Contents
Preface xi
I LOGICALPROLEGOMENA 1
1 ATwo-TierSystemofCausalReasoning 3
1.1 Aristotle’sApodeictic 5
1.2 CausationversusLogic:AnAbridgedHistory 9
1.2.1 TheLawofCausality 9
1.2.2 Leibniz’sPrincipleofSufficientReason 10
1.2.3 HumeonCausationandItsInferentialSource 11
1.2.4 Mill’sCoveringLawAccount 12
1.2.5 Hempel’sDeductive-NomologicalApproach 13
1.2.6 ASadSummary 14
1.3 OnCausalRelata 14
1.4 TheNonmonotonicRoadtoCausality 16
1.4.1 CausalAssumptionsandDefeasibility 16
1.4.2 LocalityandClosedWorldAssumption 18
1.4.3 TheCausalCalculus 20
1.5 Causation,Laws,andCounterfactuals 21
1.6 CausalityinFlux 23
2 MereologicalSemanticsforClassicalLogic 25
2.1 TwoPerspectivesofClassicalLogic 26
2.1.1 AModel-TheoreticView 27
2.2 MereologicalSemantics 30
2.3 ClassicalScottConsequence 32
2.3.1 Classicality 34
2.3.2 Axiomatization 36
2.3.3 Completeness 37
vi Contents
2.4 StandardConnectives 38
2.4.1 WhatIsaClassicalConnective? 38
2.4.2 Necessity,Dependence,andIndependence 39
2.5 PossibleWorldsSemantics 41
2.6 ComparativeSimilaritySemantics 42
2.6.1 LanguageCorrespondences 44
2.6.2 OnLewis’sDefinitionofCausation 45
2.7 Conclusions 46
2.A Appendix:ProofsoftheMainResults 47
3 Assumption-BasedNonmonotonicReasoning 53
3.1 DefaultLogic 55
3.1.1 DefaultLogicSimplified 57
3.2 ArgumentationTheory 59
3.2.1 LogicinArgumentation 61
3.2.2 CollectiveArgumentation 62
3.2.3 NonmonotonicSemantics 64
3.2.4 Negation,Deduction,andAssumptions 65
3.2.5 DefaultArgumentation 68
3.2.6 LogicProgramming 70
3.3 TheProblemofDefeasibleEntailment 71
II THEBASICS 77
4 CausalCalculus 79
4.1 ProductionInference 79
4.1.1 LogicalSemanticsofCausalRules 81
4.1.2 RegularInference 82
4.2 NonmonotonicSemanticsofCausalTheories 85
4.3 DeterminateandLiteralCausalTheories 89
4.4 BasicandCausalInference 92
4.4.1 PossibleWorldsSemantics 93
4.4.2 CausalInference 94
4.5 CausalNonmonotonicSemantics 96
4.5.1 DefaultsandExogenousPropositions 98
4.5.2 Completion 99
4.5.3 OnNondeterminateCausalTheoriesandScientificLaws 101
4.6 OnCausalInterpretationofLogicPrograms 104
4.7 NegativeCausationandNegativeCompletion 107
4.8 DefeasibleCausalityandDeepRepresentation 111
Contents vii
4.9 CausalReasoningasArgumentation 114
5 StructuralEquationModels 117
5.1 StructuralEquationsandCausalModels 118
5.2 RepresentingStructuralEquationsbyCausalRules 122
5.2.1 PropositionalCase 122
5.2.2 First-OrderCase 124
5.3 CausalCounterfactuals 126
5.3.1 Interventions,Contractions,andRevisions 126
5.3.2 TheFormalizationandSomeComparisons 127
5.4 Intervention-EquivalenceandBasicInference 131
5.5 CausalModelsandDialecticalArgumentation 134
5.5.1 AbstractDialecticalFrameworks 135
5.5.2 TheCausalRepresentationofADFs 136
5.5.3 GeneralCorrespondences 138
5.6 Conclusions 139
6 IndeterminateCausation 141
6.1 Introduction 141
6.2 DisjunctiveCausalRelations 143
6.3 SingularCausalInference 147
6.4 StableSemantics 150
6.5 CoveringSemantics 154
6.5.1 Normalization 157
6.5.2 CausalCovers 159
6.6 Summary 162
6.A Appendix:ProofsoftheMainResults 162
III EXPLANATORYCAUSALREASONING 173
7 Abduction 175
7.1 AbductiveSystemsandAbductiveSemantics 176
7.2 AbductiveProductionInference 178
7.2.1 Quasi-AbductiveCausalInference 180
7.3 AbductioninLiteralCausalTheories 182
7.4 AbductiveCausalInference 183
7.5 ClassicalAbduction 184
8 ActualCausality 187
8.1 AnOverview 188
8.2 CausalRegularityApproach 192
viii Contents
8.3 TheCausalNESSTest 195
8.3.1 Forgetting 197
8.4 ActualSubtheoriesandCausalInference 199
8.5 ExamplesandCounterexamples 201
8.5.1 Overdetermination 202
8.5.2 Switches 204
8.6 NegativeCausality 207
8.6.1 PreventionandPreemption 207
8.6.2 PreventiveOverdetermination 215
8.6.3 TheProblemofDoublePreventions 217
8.7 OnCompositeOverdetermination 224
8.8 CausalityamongMultivaluedPropositions 226
8.9 InterimConclusions 229
9 RelativeCausality 231
9.1 CausesversusConditions 232
9.2 TheAccountofHartandHonoré 234
9.3 RelativeModels 236
9.4 ProximateCauses 238
9.5 FurtherExamples 240
9.5.1 NegationasDefault 243
9.5.2 MakingaDifference 245
9.5.3 Novusactusinterveniens 247
9.6 NegativeCausalityRevisited 248
9.6.1 TriggeringandAbortion 249
9.6.2 DoublePreventionReconsidered 251
IV DYNAMICCAUSALREASONING 253
10 CausalDynamicFormalisms 255
10.1 DynamicCausalInference 257
10.1.1 StructuralDynamicCalculus 258
10.1.2 Sequentiality 264
10.1.3 DeterministicInference 266
10.1.4 OnDynamicInferencewithStatesandTransitions 268
10.2 SequentialDynamicLogic 270
10.2.1 TheLanguageandSemantics 271
10.2.2 SDLversusPDL 274
10.2.3 SequentialDynamicCalculus 277
10.2.4 Iteration 280
Contents ix
10.A Appendix:ProofsoftheMainResults 283
11 DynamicMarkovAssumption 293
11.1 DynamicMarkovPrinciple 294
11.1.1 Semantics:TransparentModels 295
11.2 BasicActionTheoriesandMarkovCompletion 296
11.3 AdmissibleQueries 299
11.4 InferentialMarkovProperty 300
11.5 MarkovPropertyandRegression 302
11.6 Summary 304
12 DynamicCausalCalculus 307
12.1 DynamicCausalCalculus 308
12.1.1 NonmonotonicTransitionSemantics 309
12.1.2 LiteralDynamicCausalTheories 313
12.2 TransitionInferenceRelation 313
12.2.1 APossibleWorldsSemantics 314
12.2.2 Correspondences 316
12.3 ComparisonswithActionLanguagesAandB 317
12.4 RepresentingActionLanguageC 320
12.4.1 AnOverviewofC+ 321
12.4.2 TheRepresentationandComparisons 324
12.4.3 PersistentActionDomains 327
12.5 Summary 329
Bibliography 331
Index 347