Actual Causality

Actual Causality

by Joseph Y. Halpern

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Overview

A new approach for defining causality and such related notions as degree of responsibility, degrees of blame, and causal explanation.

Causality plays a central role in the way people structure the world; we constantly seek causal explanations for our observations. But what does it even mean that an event C “actually caused” event E? The problem of defining actual causation goes beyond mere philosophical speculation. For example, in many legal arguments, it is precisely what needs to be established in order to determine responsibility. The philosophy literature has been struggling with the problem of defining causality since Hume.

In this book, Joseph Halpern explores actual causality, and such related notions as degree of responsibility, degree of blame, and causal explanation. The goal is to arrive at a definition of causality that matches our natural language usage and is helpful, for example, to a jury deciding a legal case, a programmer looking for the line of code that cause some software to fail, or an economist trying to determine whether austerity caused a subsequent depression.

Halpern applies and expands an approach to causality that he and Judea Pearl developed, based on structural equations. He carefully formulates a definition of causality, and building on this, defines degree of responsibility, degree of blame, and causal explanation. He concludes by discussing how these ideas can be applied to such practical problems as accountability and program verification. Technical details are generally confined to the final section of each chapter and can be skipped by non-mathematical readers.

Product Details

ISBN-13: 9780262537131
Publisher: MIT Press
Publication date: 02/19/2019
Series: The MIT Press
Edition description: Reprint
Pages: 240
Sales rank: 1,159,717
Product dimensions: 6.50(w) x 8.70(h) x 0.40(d)
Age Range: 18 Years

About the Author

Joseph Y. Halpern is Professor of Computer Science at Cornell University. He is the author of Actual Causality and the coauthor of Reasoning about Knowledge, both published by the MIT Press.

Table of Contents

Preface ix

1 Introduction and Overview 1

Notes 5

2 The HP Definition of Causality 9

2.1 Causal Models 10

2.2 A Formal Definition of Actual Cause 20

2.2.1 A language for describing causality 20

2.2.2 The HP definition of actual causality 22

2.3 Examples 28

2.4 Transitivity 41

2.5 Probability and Causality 46

2.6 Sufficient Causality 53

2.7 Causality in Nonrecursive Models 56

2.8 AC2(bo)vs. AC2(bu) 58

2.9 Causal Paths 62

2.10 Proofs 64

2.10.1 Proof of Theorem 2.2.3 64

2.10.2 Proof of Proposition 2.4.6 65

2.10.3 Proof of Proposition 2.9.2 67

Notes 70

3 Graded Causation and Normality 77

3.1 Defaults, Typicality, and Normality 77

3.2 Extended Causal Models 79

3.3 Graded Causation 85

3.4 More Examples 86

3.4.1 Knobe effects 86

3.4.2 Bogus prevention 88

3.4.3 Voting examples 91

3.4.4 Causal chains 92

3.4.5 Legal doctrines of intervening causes 94

3.5 An Alternative Approach to Incorporating Normality 97

Notes 102

4 The Art of Causal Modeling 107

4.1 Adding Variables to Structure a Causal Scenario 108

4.2 Conservative Extensions 114

4.3 Using the Original HP Definition Instead of the Updated Definition 116

4.4 The Stability of (Non-)Causality 117

4.5 The Range of Variables 123

4.6 Dependence and Independence 124

4.7 Dealing With Normality and Typicality 126

4.8 Proofs 127

4.8.1 Proof of Lemma 4.2.2 127

4.8.2 Proof of Theorem 4.3.1 128

4.8.3 Proofs and example for Section 4.4 131

Notes 135

5 Complexity and Axiomatization 139

5.1 Compact Representations of Structural Equations 140

5.2 Compact Representations of the Normality Ordering 142

5.2.1 Algebraic plausibility measures: the big picture 143

5.2.2 Piggy-backing on the causal model 148

5.3 The Complexity of Determining Causality 151

5.4 Axiomatizing Causal Reasoning 154

5.5 Technical Details and Proofs 158

5.5.1 Algebraic plausibility measures: the details 158

5.5.2 Proof of Theorems 5.3.1(c) and 5.3.2(b) 160

5.5.3 Proof of Theorems 5.4.1, 5.4.2, and 5.4.4 161

Notes 167

6 Responsibility and Blame 169

6.1 A Naive Definition of Responsibility 171

6.2 Blame 173

6.3 Responsibility Normality, and Blame 179

Notes 183

7 Explanation 187

7.1 Explanation: The Basic Definition 188

7.2 Partial Explanations and Explanatory Power 192

7.3 The General Definition of Explanation 199

Notes 201

8 Applying the Definitions 203

8.1 Accountability 204

8.2 Causality in Databases 205

8.3 Program Verification 207

8.4 Last Words 211

Notes 212

References 215

Index 225

What People are Saying About This

L. A. Paul

In this book, Joseph Halpern, a leading theorist of causality, develops a formal approach that revises and extends his earlier seminal work on counterfactual-based models for causation. The book includes a very informative, clear, and interesting discussion of the role and application of different features of causal models, and presents a new approach to modeling the causal features of responsibility, blame, and explanation. It is an important contribution to debates in philosophy and psychology about the nature of causal modeling and its application to real-world causation.

From the Publisher

How do we decide that someone is to blame for some misfortune, or that someone deserves credit for a favorable turn of events? Answering these questions and others depends on understanding how people represent and reason about the causal structure underlying specific events. The problem has plagued philosophers, legal and moral theorists, as well as psychologists. Recent years have seen enormous progress on this problem by using structural equations to model causal structure and defining causal relations in terms of counterfactuals. Much of this progress is due to the seminal work of Joe Halpern. His theories of blame and responsibility assignment and epistemic explanation are developed and expounded with full formal rigor in this seminal contribution.

Steven Sloman , Professor, Brown University, author of Causal Models: How People Think About the World and Its Alternatives and the forthcoming School of Thought: The Illusion of Knowledge and the Power of Collective Intelligence

What it might mean to say that some event was an 'actual cause' of some outcome—a conclusion that can be of crucial importance in deciding a legal case—is surprisingly difficult to characterize. This unique book describes the author's thoughtful quest to capture these subtleties in a formal language based on structural equations.

Philip Dawid , Emeritus Professor of Statistics, University of Cambridge

In this book, Joseph Halpern, a leading theorist of causality, develops a formal approach that revises and extends his earlier seminal work on counterfactual-based models for causation. The book includes a very informative, clear, and interesting discussion of the role and application of different features of causal models, and presents a new approach to modeling the causal features of responsibility, blame, and explanation. It is an important contribution to debates in philosophy and psychology about the nature of causal modeling and its application to real-world causation.

L. A. Paul , Eugene Falk Distinguished Professor of Philosophy, Department of Philosophy, University of North Carolina at Chapel Hill

Endorsement

In this book, Joseph Halpern, a leading theorist of causality, develops a formal approach that revises and extends his earlier seminal work on counterfactual-based models for causation. The book includes a very informative, clear, and interesting discussion of the role and application of different features of causal models, and presents a new approach to modeling the causal features of responsibility, blame, and explanation. It is an important contribution to debates in philosophy and psychology about the nature of causal modeling and its application to real-world causation.

L. A. Paul, Eugene Falk Distinguished Professor of Philosophy, Department of Philosophy, University of North Carolina at Chapel Hill

Steven Sloman

How do we decide that someone is to blame for some misfortune, or that someone deserves credit for a favorable turn of events? Answering these questions and others depends on understanding how people represent and reason about the causal structure underlying specific events. The problem has plagued philosophers, legal and moral theorists, as well as psychologists. Recent years have seen enormous progress on this problem by using structural equations to model causal structure and defining causal relations in terms of counterfactuals. Much of this progress is due to the seminal work of Joe Halpern. His theories of blame and responsibility assignment and epistemic explanation are developed and expounded with full formal rigor in this seminal contribution.

Philip Dawid

What it might mean to say that some event was an 'actual cause' of some outcome—a conclusion that can be of crucial importance in deciding a legal case—is surprisingly difficult to characterize. This unique book describes the author's thoughtful quest to capture these subtleties in a formal language based on structural equations.

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