Human Compatible: Artificial Intelligence and the Problem of Control

by Stuart Russell

There are two kinds of logic that really matter in computer science. The first, called propositional or Boolean logic, was known to the Greeks as well as to ancient Chinese and Indian philosophers. It is the same language of AND gates, NOT gates, and so on that makes up the circuitry of computer chips. In a very literal sense, a modern CPU is just a very large mathematical expression—hundreds of millions of pages—written in the language of propositional logic. The second kind of logic, and the one that McCarthy proposed to use for AI, is called first-order logic.B The language of first-order logic is far more expressive than propositional logic, which means that there are things that can be expressed very easily in first-order logic that are painful or impossible to write in propositional logic. For example, the rules of Go take about a page in first-order logic but millions of pages in propositional logic. Similarly, we can easily express knowledge about chess, British citizenship, tax law, buying and selling, moving, painting, cooking, and many other aspects of our commonsense world.