Proposicional

Proposicional is an adjective used in logic and linguistics to refer to propositions or to theories and constructions that relate to them. In logic, the term most often refers to propositional logic, the formal study of propositions and their connectives. A proposition is represented by a propositional variable (p, q, r, …); more complex statements are built with connectives such as negation (not), conjunction (and), disjunction (or), implication (if… then), and biconditional (if and only if). Formulas are called well-formed formulas; their meaning is defined by a truth-functional semantics: given truth values for the variables, the connective rules determine the value of every formula. Truth tables summarize these relations.

A basic propositional calculus provides rules of inference, such as Modus Ponens and various axiom schemes, to derive valid conclusions. Key concepts include tautologies (formulas true in every valuation), satisfiability (existence of a valuation making a formula true), and unsatisfiability. Equivalents like conjunctive normal form (CNF) and disjunctive normal form (DNF) facilitate algorithmic processing. The subject has formal properties such as soundness (all derivable formulas are valid) and completeness (all valid formulas are derivable).

Historically, propositional logic traces to Boolean algebra (George Boole) and was developed further by Frege, and later by Russell and Whitehead in Principia Mathematica, shaping modern logic and computer science. In practical terms, it underpins digital circuits, programming, and automated reasoning. In philosophy, it is also used to analyze propositional attitudes such as belief or intention. See also: propositional logic, Boolean algebra, predicate logic.