In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P.

In mathematics, a filter on a set X informally gives a notion of which subsets A \subseteq X are "large". Filter quantifiers are a type of logical quantifier which, informally, say whether or not a statement is true for "most" elements of X.

Unrestricted Hartree–Fock (UHF) theory is the most common molecular orbital method for open shell molecules where the number of electrons of each spin are not equal. While restricted Hartree–Fock theory uses a single molecular orbital twice, one multiplied by the α spin function and the other multiplied by the β spin function in the Slater determinant, unrestricted Hartree–Fock theory uses different molecular orbitals for the α and β electrons.

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In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers.

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<logic> An operator in predicate logic specifying for which values of a variable a formula is true. Universally quantified means "for all values" (written with an inverted A, LaTeX forall) and existentially quantified means "there exists some value" (written with a reversed E, LaTeX exists). To be unambiguous, the set to which the values of the variable belong should be specified, though this is often omitted when it is clear from the context (the "universe of discourse"). E.g. Forall x . P(x) <=> not (Exists x . not P(x)) meaning that any x (in some unspecified set) has property P which is equivalent to saying that there does not exist any x which does not have the property. If a variable is not quantified then it is a free variable. In logic programming this usually means that it is actually universally quantified. See also first order logic. (2002-05-21)