Formal Logic gives us tools for precisely describing and analyzing logical statements. Real-world problems are usually given to us in English. In order to apply our new tool, we must first “formalize” the problem by translating the statement into Logic. Then, we can analyze it using tools such as truth tables or SAT solvers.
In this topic, we will learn a new way to reason about facts in logic. Previously, we saw how to show that various facts are equivalent. Here, we will see how to infer new facts from known ones using a “proof”. This includes equivalence as a special case (when we can infer either fact from the other) but is vastly more powerful.
We will begin by writing our proofs formally, using inference rules. This makes them easy to check. Fterward, we will begin learning how to write English proofs by translating our formal proofs into English. As the course continues, we aim to get more confortable writing proofs directly in English, without working formally.
More topics will be added here as the course continues...