Artificial Intelligence/Logic/Representation

Thoughts are complex things. In AI, logic is a way to simplify thoughts to their essences in a formal manner so that they can be reasoned about by machines. Like any representation, logical representations ignore some details and make a big deal out of others.

We will discuss propositional logic, and then predicate logic. But here we'll just give you a taste of what they are like.

Let's suppose you have a thought: "Ocelots are endangered." Propositional logic would represent this with a single letter, for example, "P."

$$ P $$

Note that it ignores the fact that Ocelots are animals, that there is more than one, etc. In predicate logic, we might represent this fact like this:

$$ Endangered(Ocelots) $$

Notice that in predicate logic we have more structure. This is more powerful, and in AI, this makes it slightly less efficient. In AI, there is often a tradeoff between representational power and complexity and computational efficiency.