bound variable
Quick Summary
In logic, a bound variable is a variable that appears within the scope of a quantifier, such as "for all" or "there exists." This means its value is determined by the quantifier and it cannot be freely substituted with a constant. Variables that are not bound are called free variables.12
Quantifiers are used to specify the quantity of elements in a proposition. The universal quantifier (∀) indicates that a statement holds for all values of a variable, while the existential quantifier (∃) indicates it holds for at least one value. For example, in the statement "For all x, if x is a dog, then x is a mammal," 'x' is a bound variable.23
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formal logicThe lower predicate calculusIf a is any individual variable and α is any wff, every occurrence of a in α is said to be bound (by the quantifiers) when occurring in the wffs (∀a)α and (∃a)α. Any occurrence of a variable that is not bound is said to be free. Thus, in (∀x)(ϕx…
Read MoreIf a is any individual variable and α is any wff, every occurrence of a in α is said to be bound (by the quantifiers) when occurring in the wffs (∀a)α and (∃a)α. Any occurrence of a variable that is not bound is said to be free. Thus, in (∀x)(ϕx…
Read More- formal logicLogical manipulations in LPC
…is known as relettering a bound variable. If β is the result of relettering a bound variable in a wff α, then α and β are said to be bound alphabetical variants of each other, and bound alphabetical variants are always equivalent. The reason for restricting the replacement variable to…
Read More…is known as relettering a bound variable. If β is the result of relettering a bound variable in a wff α, then α and β are said to be bound alphabetical variants of each other, and bound alphabetical variants are always equivalent. The reason for restricting the replacement variable to…
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