Propositional logic

A formal system that represents statements as propositions and studies how their truth values combine through logical connectives. Its formulas do not analyze the internal structure of propositions.

Proposition: A declarative statement that is either true or false. Propositional logic treats these truth-valued statements as its basic units.
Logical consequence: A relation in which a conclusion must be true whenever all its premises are true. It captures when propositional premises guarantee a conclusion under every truth assignment.
Boolean circuit: A network of logic gates that computes a Boolean function from binary inputs. Each gate implements a connective, so a circuit realizes a propositional formula.
Predicate logic: A formal system that represents objects, properties, and relations using predicates and quantifiers. Unlike propositional logic, it can analyze the internal structure of statements.
Stoic logic: An ancient Greek system of logic that emphasized propositions and their combinations. Stoic thinkers developed early analyses of compound propositions and inference.
Logical connective: An operator that combines or modifies propositions to form compound propositions. Connectives build formulas whose truth depends on their component propositions.
Modus ponens: An inference rule that derives B from A and A implies B. This basic rule derives conclusions from conditionals in propositional proofs.
SAT solver: A program that determines whether a propositional formula has a satisfying assignment. SAT solvers apply propositional reasoning to large constraint systems.
Modal logic: A family of formal systems that adds operators for notions such as necessity and possibility. Its modal operators express distinctions that truth-functional connectives cannot capture.
Chrysippus: A third-century BCE Stoic philosopher renowned for his work on logic. His work helped shape ancient propositional reasoning, though much survives only indirectly.

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