- Propositional logic is a formal system for representing and reasoning about propositions. A proposition is a statement that is either true or false, but not both. Propositional logic provides a way to combine propositions to form new propositions, and to determine the truth value of new propositions from the truth value of the propositions that were used to form them.
- It is a deductive system, which means that it is based on the principle of deduction. Deduction is a process of reasoning from premises to a conclusion. In propositional logic, the premises are propositions, and the conclusion is a proposition that is derived from the premises.
- It is a formal system, which means that it has a precisely defined syntax and semantics. The syntax of propositional logic is the set of rules for constructing valid propositions. The semantics of propositional logic is the set of rules for determining the truth value of propositions.
- It is a decidable system, which means that there is an algorithm for determining whether or not a given proposition is true.
- It is not expressive enough to represent many natural language statements. For example, propositional logic cannot represent statements about the order of events, or statements about the existence of objects.
- It is not powerful enough to represent many common logical arguments. For example, propositional logic cannot represent arguments that involve quantifiers, such as "All men are mortal" or "Some men are tall."