Propositional logic
branch of logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called first-order propositional logic to contrast it with System F, but it is distinct from first-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional, and negation. Some sources include other connectives, as in the table below.
Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic.
Propositional logic is typically studied with a formal language, in which propositions are represented by letters, which are called propositional variables.
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