only bounded quantifiers, but not separation for other formulas. In KP the motivation is the fact that whether a set x satisfies a bounded quantifier formula...

quantifiers which are restricted ("bounded") to range only over the subtypes of a particular type. Bounded quantification is an interaction of parametric...

most common quantifiers are the universal quantifier and the existential quantifier. The traditional symbol for the universal quantifier is "∀", a rotated...

typically obtained by requiring that quantifiers be bounded in the induction axiom or equivalent postulates (a bounded quantifier is of the form ∀x ≤ t or ∃x ≤ t...

known as F-bound polymorphism, and it is a form of F-bounded quantification. The technique was formalized in 1989 as "F-bounded quantification." The name...

recursive function f {\displaystyle f} . This is because allowing bounded quantifier adds nothing to the definition: for a primitive recursive f {\displaystyle...

PSPACE proof where no more than one universal quantifier is placed between each variable's use and the quantifier binding that variable. This was critical...

{\displaystyle x^{y}} , together with induction for formulas with bounded quantifiers. EFA is a very weak logical system, whose proof theoretic ordinal...

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least...

In logic a branching quantifier, also called a Henkin quantifier, finite partially ordered quantifier or even nonlinear quantifier, is a partial ordering...

with each quantifier block limited to j variables. '<' is considered to be quantifier-free; here, bounded quantifiers are counted as quantifiers. PA(1, j)...

"for all x, if x is a man, then x is mortal"; where "for all x" is a quantifier, x is a variable, and "... is a man" and "... is mortal" are predicates...

function is obtained by changing the universal quantifier into an existential quantifier and negating the quantified formula. That is, ¬ ∀ x P ( x ) is equivalent...

subsets of V(*R); what this means in practice is that bounded quantification, where the bound is an internal set, never ranges over these sets. Example:...

axiom, there is also another formulation using a universal quantifier. Also using bounded Separation, the two axioms just stated together imply the existence...

listed above can be expressed in similar ways; for example, the universal quantifier ∀ x ∈ S   P ( x ) {\displaystyle \forall x\in S\ P(x)} can be thought...

bounded quantifiers beginning with existential quantifiers, alternating n − 1 {\displaystyle n-1} times between existential and universal quantifiers...

types, so that multiple can be used with a single implementation Bounded quantification, restricts type parameters to a range of subtypes Subtyping, different...

of hyponymy and holonymy. It is also related to the concept of bounded quantification in mathematical logic (see Order-sorted logic). Subtyping should...

possible world, a concept corresponds to a modal proposition, and a role-bounded quantifier to a modal operator with that role as its accessibility relation....

scope of a quantifier or connective is the shortest formula in which it occurs, determining the range in the formula to which the quantifier or connective...

undefined behavior, infinite recursion, or unrecoverable errors. In Bounded Quantification with Bottom, Pierce says that "Bot" has many uses: In a language...

polymorphism and subtyping leads to the concepts of variance and bounded quantification. Row polymorphism is a similar, but distinct concept from subtyping...

certain condition. This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the...

universal class, or universe, is the class of all sets. A universal quantifier is the quantifier "for all", usually written ∀ unordered pair A set of two elements...

S2CID 26425651. Retrieved 25 October 2022. Pierce, Benjamin C. (1997). "Bounded Quantification with Bottom". Indiana University CSCI Technical Report (492): 1...

precompact or totally bounded if for every r > 0 there is a finite cover of M by open balls of radius r. Every totally bounded space is bounded. To see this,...

type. branching quantifier A type of quantifier in formal logic that allows for the expression of dependencies between different quantified variables, representing...

expressed in two ways. There is an existential quantifier, ∃, meaning some. There is also a universal quantifier, ∀, meaning every, each, or all. Ambiguity...

integrated into a PP. Structurally, a quantifier is followed by a noun, and a preposition in between denotes the quantifier is a subset of the following noun...