Essential Math for AI

Chapter 12. Mathematical Logic

Humans bend the rules.

H.

Historically in the AI field, logic-based agents come before machine learning and neural network–based agents. The reason we went over machine learning, neural networks, probabilistic reasoning, graph representations, and operations research before logic is that we want to tie it all into one narrative of reasoning within an agent, as opposed to thinking of logic as old and neural networks as modern. We want to view the recent advancements as enhancing the way a logical AI agent represents and reasons about the world. A good way to think about this is similar to enlightenment: an AI agent used to reason using the rigid rules of handcoded knowledge base and handcoded rules to make inferences and decisions, then suddenly it gets enlightened and becomes endowed with more reasoning tools, networks, and neurons that allow it to expand both its knowledge base and inference methods. This way, it has more expressive power and can navigate more complex and uncertain situations. Moreover, combining all the tools would allow an agent the option to sometimes break the rules of a more rigid logic framework and employ a more flexible one, depending on the situation, just like humans. Bending, breaking, and even changing the rules are distinctive human attributes.

The dictionary meaning of the word logic sets the tone for this chapter and justifies its progression.

Logic

A framework that organizes the rules and processes used for sound ...