Existential quantification
Existential quantification asserts that at least one object in a specified domain satisfies a predicate, usually written ∃.
Predicate logic: A formal system that represents objects, properties, relations, and quantification. Existential quantification is an operator in this broader logical system.
First-order logic: A formal logic with variables for objects, predicates, and quantifiers over a domain. Existential quantification is one of its two standard quantifiers.
Universal quantification: The logical operation asserting that every object in a domain satisfies a predicate, usually written ∀. It requires every domain member to qualify, not merely one.
Existential instantiation: A proof rule that introduces a fresh name for an object asserted to exist. It uses an existential premise by temporarily naming a witness.
Quantifier: A logical expression that specifies how many objects satisfy a condition. Existential quantification is the at-least-one form of quantification.
Atomic formula: A formula formed by applying a predicate to terms, without logical connectives or quantifiers. An existential quantifier can bind a variable in an atomic formula.
Unique existence: The claim that exactly one object in a domain satisfies a predicate, often written ∃!. It adds an at-most-one requirement to ordinary existential quantification.
Existence proof: A mathematical proof establishing that at least one object with specified properties exists. Such proofs establish the truth of existentially quantified claims.
Domain of discourse: The collection of objects over which variables in a logical expression range. The domain determines which objects can witness an existential claim.
Logical connective: An operator such as negation, conjunction, or disjunction that combines or modifies propositions. Connectives combine existential claims with other formulas.