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Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles: e.g., two dozen or more than a score. Scientific non-numerical quantities are represented as SI units.
Most determiners are very basic in their morphology, but some are compounds. [1]: 391 A large group of these is formed with the words any, every, no, and some together with body, one, thing, or where (e.g., anybody, somewhere). [1]: 411 The morphological phenomenon started in Old English, when thing, was combined with some, any, and no.
[1] [2] Examples in English include articles (the and a), demonstratives (this, that), possessive determiners (my, their), and quantifiers (many, both). Not all languages have determiners, and not all systems of grammatical description recognize them as a distinct category.
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 in the first order formula () expresses that everything in the domain satisfies the property denoted by .
t may contain some, all or none of the x 1, …, x n and it may contain other variables. In this case we say that function definition binds the variables x 1, …, x n. In this manner, function definition expressions of the kind shown above can be thought of as the variable binding operator, analogous to the lambda expressions of lambda calculus.
Quantifiers in semantics – such as the quantifier in the antecedent of a bound variable pronoun – can be expressed in two ways. There is an existential quantifier, ∃, meaning some. There is also a universal quantifier, ∀, meaning every, each, or all. Ambiguity arises when there are multiple quantifiers in one sentence.
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases . For example, the generalized quantifier every boy denotes the set of sets of which every boy is a member: { X ∣ ∀ x ( x is a boy → x ∈ X ) } {\displaystyle \{X\mid \forall x ...
Filter quantifiers are a type of logical quantifier which, informally, say whether or not a statement is true for "most" elements of . Such quantifiers are often used in combinatorics , model theory (such as when dealing with ultraproducts ), and in other fields of mathematical logic where (ultra)filters are used.