## Causality. Models, reasoning, and inference. 2nd revised ed.(English)Zbl 1188.68291

Cambridge: Cambridge University Press (ISBN 978-0-521-89560-6/hbk). xviii, 464 p. (2009).
This book presents a philosophically well-founded mathematical approach to causality and causal reasoning. At the heart of this book there is the question of how humans discover, test and argue about causation.
The first three chapters contain the necessary background in probability theory and graph theory to understand the later chapters. Furthermore, the author discusses how to discover cause-effect relationships in raw data. To aid such discoveries in case some causal knowledge is available the Back-Door and Front-Door criteria are introduced.
Using these criteria and the $$do(\cdot)$$-operator, the author shows in chapter four how to deal with problems of identifiability.
In chapter six, the author shows how the developed framework can be used to solve Simon’s paradox.
The following two chapters are devoted to counterfactuals. Using counterfactuals, the relationship between necessary and sufficient components of causality are analyzed. It is then shown how data from experimental and nonexperimental studies can be combined to yield information that neither study alone can reveal.
The next chapter gives an explication of the notion of “actual cause”, which is particular interesting if there is more than one possible cause.
The last chapter contains a transcript of a public lecture by the author providing a historical and conceptual introduction to his work
The technical centerpiece of this book is the $$do(\cdot)$$-operator and the three-step construction of 1) abduction, 2) action and 3) prediction. This construction on causal models is used to reason about 1) predictions, 2) interventions and 3) counterfactuals.
At the philosophical heart of the book there is the observation that a purely mathematical interpretation of an equation of the form $$y=\beta x$$ does not allow to read-off a cause-effect relationship between $$Y$$ and $$X.$$ The author strongly supports the view that only a mathematical language that permits the handling of causal information is suitable to deal with problems of causality and counterfactuals.
The mathematical proofs and philosophical considerations in this book are not only relevant to mathematicians, computer scientists and philosophers, but also to statisticians, economists, epidemiologists, politicians, lawyers and judges. Many examples throughout the text show how to apply the formal methods to real-world problems. For instance, one such problem is the approval of new drugs.
Compared to the first edition (2000; Zbl 0959.68116), this second condition contains summaries of developments of the last eight years. Furthermore, an eleventh chapter has been added in which the author provides supplementary material discussing queries concerning the first edition of the book.
In this chapter, the author gives a daring statement summarizing his scientific work: “If I am remembered for no other contribution except for insisting on the casual-statistical distinction, I would consider my scientific work worthwhile.”

### MSC:

 68T37 Reasoning under uncertainty in the context of artificial intelligence 03A99 Philosophical aspects of logic and foundations 03B48 Probability and inductive logic 68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) 68T30 Knowledge representation 03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations 68-02 Research exposition (monographs, survey articles) pertaining to computer science

Zbl 0959.68116

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