Paraconsistent logic

Paraconsistent logic is a logic in which contradictions do not entail every proposition. It permits reasoning with inconsistent information without collapsing into triviality.

Negation: A logical operation that forms a proposition's denial. Paraconsistent logics often alter how negation interacts with contradiction and inference.
Aristotle: An ancient Greek philosopher whose writings shaped logic and metaphysics. His discussion of contradiction and excluded middle frames questions later addressed by paraconsistent logicians.
Classical logic: A family of logics whose standard systems include classical negation and the principle of explosion. It supplies the familiar baseline whose explosive consequence paraconsistent logic blocks.
Inconsistent database: A database whose constraints or stored facts cannot all be satisfied together. Paraconsistent query methods can extract information without making every query succeed.
Explosion principle: The rule that a contradiction entails any proposition, also called ex contradictione quodlibet. Rejecting or limiting this principle is the defining formal move of paraconsistent logic.
Sequent calculus: A proof system that derives sequents using formal inference rules. Inference rules make explicit which conclusions remain valid when premises conflict.
Graham Priest: A contemporary philosopher and logician known for work on dialetheism and non-classical logic. His work developed influential defenses of dialetheism using paraconsistent systems.
Contradiction: A pair of claims that cannot both be true under a given interpretation. Paraconsistent reasoning begins with conflicting claims but does not let them trivialize a theory.
Inconsistency-tolerant reasoning: Reasoning methods that preserve useful conclusions despite conflicting premises. It is the practical aim shared by many paraconsistent approaches.
Intuitionistic logic: A logic that rejects unrestricted use of the law of excluded middle and interprets proof constructively. It departs from classical logic for a different reason and is not generally paraconsistent.

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