The forms of inference studied by classical deductive logic represent the simpler and more common sorts of inference we make in everyday thought and speech. The goal of modern deductive logic has been to develop a more comprehensive system that allows us to analyze and evaluate more complex arguments. The characteristic features of modern theories are their use of symbols to represent the elements of logical form and their use of a small set of rules to generate and test arguments of any complexity.

Propositional logic is the logic of compound statements -- statements that are made up of other, simpler propositions.

Propositional logic is one main branch of what is known as symbolic logic. In earlier chapters, we used symbols such as p and q for propositions, S and P for terms. We symbolized the content of propositions. However, we did not symbolize the logical forms of propositions and arguments; we used words like "all," "some," "if . . . then," "or." Modern symbolic logic replaces all of these with symbols. In this respect, it is like mathematics, which not only uses variables to represent numbers, but also uses special symbols for operations like addition or multiplication that we can perform on numbers.