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. The previous chapters considered learning probabilities, which is useful by itself when many similar cases have been observed, however novel situations require reasoning, not just learning. This chapter considers reasoning with uncertainty that is required whenever an intelligent agent is not omniscient, and cannot just rely on having seen similar situations many times.