Logictruefalse

Logictruefalse is a term used to describe a two-valued propositional logic that operates with the binary truth values true and false. As a simplified model of classical propositional logic, it focuses on the evaluation of well-formed formulas through truth-functional connectives and valuations.

The formal language includes a set of propositional variables and connectives such as not, and, or, implies, and biconditional. Formulas are constructed recursively from variables by applying these connectives. For example, (p and q) -> r is a typical formula in logictruefalse.

Semantics assign to each variable a value in {true, false} via a valuation function. The truth value of a formula is computed by standard truth tables: not flips a value; and requires both operands to be true; or requires at least one true; implies is defined as not P or Q; biconditional as P if and only if Q. A formula is tautologically true (a tautology) when it evaluates to true under every valuation.

Axioms and rules of inference may be given in a Hilbert-style system or in natural deduction. Common choices ensure that all tautologies are provable, making logictruefalse semantically complete with respect to truth-valuations.

Relation to other logics: logictruefalse corresponds closely to classical propositional logic and is often used as an introductory vehicle for boolean algebra and digital logic. Applications include teaching basic logic, reasoning about computer programs, and formulating SAT problems. See also boolean algebra, propositional logic, truth table.