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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.
For example, it is intuitively clear that if: Some cat is feared by every mouse. then it follows logically that: All mice are afraid of at least one cat. The syntax of traditional logic (TL) permits exactly four sentence types: "All As are Bs", "No As are Bs", "Some As are Bs" and "Some As are not Bs". Each type is a quantified sentence ...
This function typically comes before any modifiers in the NP (e.g., some very pretty wool sweaters, not *very pretty some wool sweaters [a]). The determinative function is typically obligatory in a singular, countable, common noun phrase (compare I have a new cat to *I have new cat).
Augustus De Morgan confirmed this in 1847, but modern usage began with De Morgan in 1862 where he makes statements such as "We are to take in both all and some-not-all as quantifiers". [ 13 ] Gottlob Frege , in his 1879 Begriffsschrift , was the first to employ a quantifier to bind a variable ranging over a domain of discourse and appearing in ...
[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.
Many words of different parts of speech indicate number or quantity. Such words are called quantifiers. Examples are words such as every, most, least, some, etc. Numerals are distinguished from other quantifiers by the fact that they designate a specific number. [3] Examples are words such as five, ten, fifty, one hundred, etc.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃ x " or " ∃( x ...
For example, one can write the meaning of sleeps as the following lambda expression, which is a function from an individual x to the proposition that x sleeps. λ x . s l e e p ′ ( x ) {\displaystyle \lambda x.\mathrm {sleep} '(x)} Such lambda terms are functions whose domain is what precedes the period, and whose range are the type of thing ...