Quantificational

Quantificational is a term used in linguistics and logic to describe expressions that specify quantity over a domain of entities. Quantificational expressions include determiners and numerals such as every, some, most, no, two, three, and other terms that constrain how many individuals satisfy a given predicate. When combined with a noun, they form a quantifier phrase that contributes the truth-conditions of a sentence by binding variables in its logical representation.

In semantics, quantificational expressions are analyzed as introducing a relation between a set of individuals and a property. In formal logic, the most familiar cases are universal and existential quantifiers, expressed by words like "every" and "some." Generalized quantifiers extend this idea to meanings such as "most," "few," or "at least three." The exact truth of a quantificational statement depends on the size or structure of the relevant set within the domain being considered.

Quantificational phrases interact with other operators such as negation and modality, often producing scope phenomena and potential ambiguity. For example, sentences like "Every student read a book" can be interpreted with different quantifier scopes, yielding distinct logical forms and, in many languages, different surface readings. Quantificational expressions are a central topic in formal semantics and philosophy of language, where they are used to model how natural language expresses quantities and how those expressions combine with predicates to determine truth conditions.

Applications of quantificational analysis appear in linguistics, logic, philosophy, and natural language processing, helping explain how languages encode quantity, scope, and generalization.