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  The Art of Causal Conjecture

Glenn Shafer
Published by MIT Press in their Artificial Intelligence Series in 1996.
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From the Book

In The Art of Causal Conjecture, Glenn Shafer lays out a new mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence, and philosophy.

The various disciplines that use causal reasoning differ in the relative weight they put on security and precision of knowledge as opposed to timeliness of action. The natural and social sciences seek high levels of certainty in the identification of causes, and high levels of precision in the measurement of their effects. The practical sciences-medicine, business, engineering, and artificial intelligence-must act on causal conjectures based on more limited knowledge. Shafer's understanding of causality contributes to both these uses of causal reasoning. His language for causal explanation can guide statistical investigation in the natural and social sciences, and it can also be used to formulate assumptions of causal uniformity needed for decision making the practical sciences.

Causal ideas permeate the use of probability and statistics in all branches of industry, commerce, government, and science. The Art of Causal Conjecture shows that causal ideas can be equally important in theory. It does not challenge the maxim that causation cannot be proven from statistics alone, but by bringing causal ideas into the foundations of probability, it allows causal conjectures to be more clearly quantified, debated, and confronted by statistical evidence.

In most domains to which artificial intelligence is applied, such as marketing and auditing, causal reasoning is essential. The Art of Causal Conjecture contributes to the task of artificial intelligence in these domains by showing how assumptions of causal uniformity can be formulated and then relaxed, and by showing how the description of causal mechanisms can be refined.

The basic idea of The Art of Causal Conjecture is to bring the probability tree, which was basic to the thinking of Pascal, Fermat, and other pioneers of probability, back into the foundations of the subject. A probability tree represents possibilities for the step-by-step evolution of an observer's knowledge. If that observer is nature, then the steps in the tree are causes, and the probabilities in the tree express nature's limited ability to predict the effects of the causes. The Art of Causal Conjecture contributes to probability as a branch of pure mathematics by showing how probability trees allow an elementary account of martingale theory, and it contributes to the philosophy of probability by showing how both belief and frequency are involved in the evolution of an observer's knowledge.

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