propozicionális

Propozicionális is an adjective used in logic to refer to propositions and the logical study of their connections. In English, this area is called propositional logic or sentential logic, a formal system that analyzes how truth-functional connectives combine simple statements into more complex ones.

A propositional language consists of a (potentially infinite) set of propositional variables, such as P, Q, and R. Formulas are built from these variables using a fixed set of connectives, most commonly negation (not), conjunction (and), disjunction (or), implication, and biconditional. The formation rules define well-formed formulas.

Semantics assigns truth values to formulas. A valuation maps each propositional variable to true or false; the truth value of any complex formula is determined recursively by the truth-functional meaning of the connectives. Common tasks include determining tautologies (always true), satisfiability (there exists a valuation making the formula true), and equivalence between formulas, often illustrated with truth tables.

Proof systems for propositional logic include Hilbert-style axiom systems and natural deduction, as well as tableaux and resolution methods used in automated reasoning. The logic is sound and complete for classical truth-functional semantics, meaning all valid formulas have proofs and all provable formulas are valid.

Propositional logic is foundational in computer science, digital circuit design, and formal verification. It models simple decision problems and underpins SAT solvers. It differs from predicate logic by lacking quantifiers and internal structure within propositions; it focuses solely on the truth-functional relation between statements.