Classical logic

Classical logic is a family of deductive systems in which propositions obey principles such as bivalence and noncontradiction. Its standard forms include classical propositional and first-order logic.

Law of excluded middle: The principle that every proposition is true or its negation is true. Classical logic accepts this principle for every proposition.
Modus ponens: An inference rule that derives Q from P and if P then Q. It is a basic rule of classical proof systems.
Intuitionistic logic: A logic that interprets proof constructively and does not generally accept the law of excluded middle. It rejects unrestricted excluded middle, distinguishing it from classical logic.
Aristotle: An ancient Greek philosopher whose works established influential systems of logic and natural philosophy. His syllogistic theory became a central source of traditional logic.
Mathematical proof: A deductive argument that establishes a mathematical statement from accepted assumptions and rules. Classical logic supplies standard rules for formal mathematical deduction.
Law of noncontradiction: The principle that a proposition and its negation cannot both be true. It rules out contradictions as jointly true in classical logic.
Truth table: A table showing a compound proposition's truth value for every assignment of values to its components. Truth tables decide validity for finite propositional arguments.
Paraconsistent logic: A logic in which contradictions do not entail every proposition. It blocks classical explosion when premises are inconsistent.
Stoic logic: An ancient Greek system of propositional reasoning developed by Stoic philosophers. It developed argument forms based on whole propositions, unlike Aristotelian syllogistics.
Boolean algebra: An algebraic structure whose operations model conjunction, disjunction, and negation. It gives classical propositional logic an algebraic representation.

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