Propositional logic allows us to analyze arguments that depend on logical relationships among compound propositions. The units of analysis are component propositions along with the truth-functional connectives. However, some arguments require a finer-grained analysis. In some cases, we need to break propositions down into their elements, and this is the function of predicate logic.

First, we examine the symbolic notation used to represent the inner structure of propositions. Then we present a few new rules of inference and see how to use them along with the propositional rules in constructing proofs.