A Logical Theory of Causality

✍ Scribed by Alexander Bochman

• Publisher: The MIT Press
• Year: 2021
• Tongue: English
• Leaves: 367
• Category: Library

✦ Table of Contents

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