A Logical Theory of Causality

Description

Contents Preface I. Logical Prolegomena 1. A Two-Tier System of Causal Reasoning 1.1 Aristotle’s Apodeictic 1.2 Causation versus Logic: An Abridged History 1.2.1 The Law of Causality 1.2.2 Leibniz’s Principle of Sufficient Reason 1.2.3 Hume on Causation and Its Inferential Source 1.2.4 Mill’s Covering Law Account 1.2.5 Hempel’s Deductive-Nomological Approach 1.2.6 A Sad Summary 1.3 On Causal Relata 1.4 The Nonmonotonic Road to Causality 1.4.1 Causal Assumptions and Defeasibility 1.4.2 Locality and Closed World Assumption 1.4.3 The Causal Calculus 1.5 Causation, Laws, and Counterfactuals 1.6 Causality in Flux 2. Mereological Semantics for Classical Logic 2.1 Two Perspectives of Classical Logic 2.1.1 A Model-Theoretic View 2.2 Mereological Semantics 2.3 Classical Scott Consequence 2.3.1 Classicality 2.3.2 Axiomatization 2.3.3 Completeness 2.4 Standard Connectives 2.4.1 What Is a Classical Connective? 2.4.2 Necessity, Dependence, and Independence 2.5 Possible Worlds Semantics 2.6 Comparative Similarity Semantics 2.6.1 Language Correspondences 2.6.2 On Lewis’s Definition of Causation 2.7 Conclusions 2.A Appendix: Proofs of the Main Results 3. Assumption-Based Nonmonotonic Reasoning 3.1 Default Logic 3.1.1 Default Logic Simplified 3.2 Argumentation Theory 3.2.1 Logic in Argumentation 3.2.2 Collective Argumentation 3.2.3 Nonmonotonic Semantics 3.2.4 Negation, Deduction, and Assumptions 3.2.5 Default Argumentation 3.2.6 Logic Programming 3.3 The Problem of Defeasible Entailment II. The Basics 4. Causal Calculus 4.1 Production Inference 4.1.1 Logical Semantics of Causal Rules 4.1.2 Regular Inference 4.2 Nonmonotonic Semantics of Causal Theories 4.3 Determinate and Literal Causal Theories 4.4 Basic and Causal Inference 4.4.1 Possible Worlds Semantics 4.4.2 Causal Inference 4.5 Causal Nonmonotonic Semantics 4.5.1 Defaults and Exogenous Propositions 4.5.2 Completion 4.5.3 On Nondeterminate Causal Theories and Scientific Laws 4.6 On Causal Interpretation of Logic Programs 4.7 Negative Causation and Negative Completion 4.8 Defeasible Causality and Deep Representation 4.9 Causal Reasoning as Argumentation 5. Structural Equation Models 5.1 Structural Equations and Causal Models 5.2 Representing Structural Equations by Causal Rules 5.2.1 Propositional Case 5.2.2 First-Order Case 5.3 Causal Counterfactuals 5.3.1 Interventions, Contractions, and Revisions 5.3.2 The Formalization and Some Comparisons 5.4 Intervention-Equivalence and Basic Inference 5.5 Causal Models and Dialectical Argumentation 5.5.1 Abstract Dialectical Frameworks 5.5.2 The Causal Representation of ADFs 5.5.3 General Correspondences 5.6 Conclusions 6. Indeterminate Causation 6.1 Introduction 6.2 Disjunctive Causal Relations 6.3 Singular Causal Inference 6.4 Stable Semantics 6.5 Covering Semantics 6.5.1 Normalization 6.5.2 Causal Covers 6.6 Summary 6.A Appendix: Proofs of the Main Results III. Explanatory Causal Reasoning 7. Abduction 7.1 Abductive Systems and Abductive Semantics 7.2 Abductive Production Inference 7.2.1 Quasi-Abductive Causal Inference 7.3 Abduction in Literal Causal Theories 7.4 Abductive Causal Inference 7.5 Classical Abduction 8. Actual Causality 8.1 An Overview 8.2 Causal Regularity Approach 8.3 The Causal NESS Test 8.3.1 Forgetting 8.4 Actual Subtheories and Causal Inference 8.5 Examples and Counterexamples 8.5.1 Overdetermination 8.5.2 Switches 8.6 Negative Causality 8.6.1 Prevention and Preemption 8.6.2 Preventive Overdetermination 8.6.3 The Problem of Double Preventions 8.7 On Composite Overdetermination 8.8 Causality among Multivalued Propositions 8.9 Interim Conclusions 9. Relative Causality 9.1 Causes versus Conditions 9.2 The Account of Hart and Honoré 9.3 Relative Models 9.4 Proximate Causes 9.5 Further Examples 9.5.1 Negation as Default 9.5.2 Making a Difference 9.5.3 Novus actus interveniens 9.6 Negative Causality Revisited 9.6.1 Triggering and Abortion 9.6.2 Double Prevention Reconsidered IV. Dynamic Causal Reasoning 10. Causal Dynamic Formalisms 10.1 Dynamic Causal Inference 10.1.1 Structural Dynamic Calculus 10.1.2 Sequentiality 10.1.3 Deterministic Inference 10.1.4 On Dynamic Inference with States and Transitions 10.2 Sequential Dynamic Logic 10.2.1 The Language and Semantics 10.2.2 SDL versus PDL 10.2.3 Sequential Dynamic Calculus 10.2.4 Iteration 10.A Appendix: Proofs of the Main Results 11. Dynamic Markov Assumption 11.1 Dynamic Markov Principle 11.1.1 Semantics: Transparent Models 11.2 Basic Action Theories and Markov Completion 11.3 Admissible Queries 11.4 Inferential Markov Property 11.5 Markov Property and Regression 11.6 Summary 12. Dynamic Causal Calculus 12.1 Dynamic Causal Calculus 12.1.1 Nonmonotonic Transition Semantics 12.1.2 Literal Dynamic Causal Theories 12.2 Transition Inference Relation 12.2.1 A Possible Worlds Semantics 12.2.2 Correspondences 12.3 Comparisons with Action Languages A and B 12.4 Representing Action Language C 12.4.1 An Overview of C+ 12.4.2 The Representation and Comparisons 12.4.3 Persistent Action Domains 12.5 Summary Bibliography Index