Artificial Intelligence: Foundations of Computational Agents,  2nd Edition

Chapter 8 Reasoning with Uncertainty

It is remarkable that a science which began with the consideration of games of chance should become the most important object of human knowledge …The most important questions of life are, for the most part, really only problems of probability …
The theory of probabilities is at bottom nothing but common sense reduced to calculus.

– Pierre Simon de Laplace [1812]

Agents in real environments are inevitably forced to make decisions based on incomplete information. Even when an agent senses the world to find out more information, it rarely finds out the exact state of the world. For example, a doctor does not know exactly what is going on inside a patient, a teacher does not know exactly what a student understands, and a robot does not know what is in a room it left a few minutes ago. When an intelligent agent must act, it has to use whatever information it has. This chapter considers reasoning with uncertainty that arises whenever an agent is not omniscient. This is used in Chapter 9 as a basis for acting with uncertainty. This chapter starts with probability, shows how to represent the world by making appropriate independence assumptions, and shows how to reason with such representations.