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.

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence ...

A general formal theory of causal reasoning as a logical study of causal models, reasoning, and inference. In this book, Alexander Bochman presents a general formal theory of causal reasoning as a logical study of causal models, reasoning, and inference, basing it on a supposition that causal reasoning is not a competitor of logical reasoning but its complement for situations lacking logically sufficient data or knowledge. Bochman also explores the relationship of this theory with the popular structural equation approach to causality proposed by Judea Pearl and explores several applications ranging from artificial intelligence to legal theory, including abduction, counterfactuals, actual and proximate causality, dynamic causal models, and reasoning about action and change in artificial intelligence. As logical preparation, before introducing causal concepts, Bochman describes an alternative, situation-based semantics for classical logic that provides a better understanding of what can be captured by purely logical means. He then presents another prerequisite, outlining those parts of a general theory of nonmonotonic reasoning that are relevant to his own theory. These two components provide a logical background for the main, two-tier formalism of the causal calculus that serves as the formal basis of his theory. He presents the main causal formalism of the book as a natural generalization of classical logic that allows for causal reasoning. This provides a formal background for subsequent chapters. Finally, Bochman presents a generalization of causal reasoning to dynamic domains.

A Turing Award-winning computer scientist and statistician shows how understanding causality has revolutionized science and will revolutionize artificial intelligence "Correlation is not causation." This mantra, chanted by scientists for more than a century, has led to a virtual prohibition on causal talk. Today, that taboo is dead. The causal revolution, instigated by Judea Pearl and his colleagues, has cut through a century of confusion and established causality -- the study of cause and effect -- on a firm scientific basis. His work explains how we can know easy things, like whether it was rain or a sprinkler that made a sidewalk wet; and how to answer hard questions, like whether a drug cured an illness. Pearl's work enables us to know not just whether one thing causes another: it lets us explore the world that is and the worlds that could have been. It shows us the essence of human thought and key to artificial intelligence. Anyone who wants to understand either needs The Book of Why.

Making a Difference presents fifteen original essays on causation and counterfactuals by an international team of experts. Collectively, they represent the state of the art on these topics. The essays in this volume are inspired by the life and work of Peter Menzies, who made a difference in the lives of students, colleagues, and friends. Topics covered include: the semantics of counterfactuals, agency theories of causation, the context-sensitivity of causal claims, structural equation models, mechanisms, mental causation, causal exclusion argument, free will, and the consequence argument.

A general formal theory of causal reasoning as a logical study of causal models, reasoning, and inference. In this book, Alexander Bochman presents a general formal theory of causal reasoning as a logical study of causal models, reasoning, and inference, basing it on a supposition that causal reasoning is not a competitor of logical reasoning but its complement for situations lacking logically sufficient data or knowledge. Bochman also explores the relationship of this theory with the popular structural equation approach to causality proposed by Judea Pearl and explores several applications ranging from artificial intelligence to legal theory, including abduction, counterfactuals, actual and proximate causality, dynamic causal models, and reasoning about action and change in artificial intelligence. As logical preparation, before introducing causal concepts, Bochman describes an alternative, situation-based semantics for classical logic that provides a better understanding of what can be captured by purely logical means. He then presents another prerequisite, outlining those parts of a general theory of nonmonotonic reasoning that are relevant to his own theory. These two components provide a logical background for the main, two-tier formalism of the causal calculus that serves as the formal basis of his theory. He presents the main causal formalism of the book as a natural generalization of classical logic that allows for causal reasoning. This provides a formal background for subsequent chapters. Finally, Bochman presents a generalization of causal reasoning to dynamic domains.

A concise and self-contained introduction to causal inference, increasingly important in data science and machine learning. The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data. After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem. The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.

This volume addresses fundamental issues in the philosophy of science in the context of two most intriguing fields: biology and economics. Written by authorities and experts in the philosophy of biology and economics, Mechanism and Causality in Biology and Economics provides a structured study of the concepts of mechanism and causality in these disciplines and draws careful juxtapositions between philosophical apparatus and scientific practice. By exploring the issues that are most salient to the contemporary philosophies of biology and economics and by presenting comparative analyses, the book serves as a platform not only for gaining mutual understanding between scientists and philosophers of the life sciences and those of the social sciences, but also for sharing interdisciplinary research that combines both philosophical concepts in both fields. The book begins by defining the concepts of mechanism and causality in biology and economics, respectively. The second and third parts investigate philosophical perspectives of various causal and mechanistic issues in scientific practice in the two fields. These two sections include chapters on causal issues in the theory of evolution; experiments and scientific discovery; representation of causal relations and mechanism by models in economics. The concluding section presents interdisciplinary studies of various topics concerning extrapolation of life sciences and social sciences, including chapters on the philosophical investigation of conjoining biological and economic analyses with, respectively, demography, medicine and sociology.

This Element provides an accessible introduction to the contemporary philosophy of causation. It introduces the reader to central concepts and distinctions (type vs token causation, probabilistic vs deterministic causation, difference-making, interventions, overdetermination, pre-emption) and to key tools (structural equations, graphs, probabilistic causal models) drawn upon in the contemporary debate. The aim is to fuel the reader's interest in causation, and to equip them with the resources to contribute to the debate themselves. The discussion is historically informed and outward-looking. 'Historically informed' in that concise accounts of key historical contributions to the understanding of causation set the stage for an examination of the latest research. 'Outward looking' in that illustrations are provided of how the philosophy of causation relates to issues in the sciences, law, and elsewhere. The aim is to show why the study of causation is of critical importance, besides being fascinating in its own right.

Actual causality is determining causation for specific events. This includes questions such as: did the pasta on the stove cause the fire alarm to go off or did the power outage cause the lights to turn off? Another example follows: If Suzie throws a rock at a bottle and later Billy throws a rock at the same bottle, a question of actual causality is, did Suzie throwing a rock cause the bottle to break? One common method to answer questions of actual causality is to evaluate the situation if the first event did not occur. This is known as a counterfactual approach. If Suzie had not thrown the rock, then the bottle would still have broken. This means that the counterfactual approach does not lead to the same conclusion that most humans arrive at. In this paper, we define a new method for questions of actual causality, which we call the causal path method. To evaluate this method, we compare it to the counterfactual approach and the expectations of humans from related work. To test this method, we use Autumn models. Autumn is a programming language for expressing causal probabilistic models that provides the infrastructure to express real-world mechanisms in code. In Autumn we are able to model and test the Billy and Suzie rock example. After evaluating the method on these Autumn models, we explore further applications for the new causal path method.