Kvantifierade

Kvantifierade is a term used in logic, mathematics and linguistics to describe a statement or expression in which a variable has been bound by a quantifier. It contrasts with a free variable, which is not bound by any quantifier. In formal logic, quantifiers are operators that indicate the number of individuals in a domain that satisfy a predicate. The two standard quantifiers are universal quantification, denoted ∀ and read “for all,” and existential quantification, denoted ∃ and read “there exists.” A variable within the scope of a quantifier is kvantifierad; the truth of the formula depends on the quantified predicate.

Example: ∀x P(x) means that P(x) holds for every x in the domain; ∃x P(x) means there exists at least one x such that P(x) holds. The order and scope of multiple quantifiers can change the meaning (for example, ∀x ∃y P(x,y) vs ∃y ∀x P(x,y)).

In linguistics and semantics, kvantifierade expressions include phrases like “everyone,” “some student,” or “most,” and their scope interacts with negation and other operators, producing quantificational ambiguity. The study of how quantifiers interact with syntax and semantics is a key area of formal semantics and logical theory, including techniques like quantifier raising and variable binding.

In practice, the concept also appears in computer science and databases, where logic-like quantification underlies queries that test “exists” or “for all” conditions.