What is conditional event algebra and why should you care?

Building practical intelligent-system algorithms requires appropriate tools for capturing the basic features of highly complex real-world environments. One of the most important of these tools, probability theory, is a calculus of events (e.g. EVENT = 'A fire-control radar of type A is detected' with Prob(EVENT) = 0.80). Conditional Event Algebra (CEA) is a relatively new inference calculus which rigorously extends standard probability theory to include events which are contingent-e.g. rules such as 'If fire-control radar A is detected, then weapon B will be launched'; or conditionals such as 'observation Z given target state X.' CEA allows one to (1) probabilistically model a contingent event; (2) assign a probability Prob(COND_EVENT) = 0.50 to it; and (3) compute with such conditional events and probabilities using the same basic rules that govern ordinary events and probabilities. Since CEA is only about ten years old, it has achieved visibility primarily among specialists in expert-systems theory and mathematical logic. Recently, however, it has become clear that CEA has potentially radical implications for engineering practice as well. The purpose of this paper is to bring this promising new tool to the attention of the wider engineering community. We will give a tutorial introduction to CEA, based on simple motivational examples, and describe its potential applications in a number of practical engineering problems.