Completely free variable
A variable is called completely free in a formula of predicate logic if it occurs in at least one place in the formula but is not quantified anywhere within the formula .
The distinction between free and fully free variables is of a technical nature. It is of no relevance to the logical meaning of a formula, as any formula can be converted into a logically equivalent one by renaming it, in which all free variables are actually completely free.
Examples
- Both and are completely free variables in the formula .
- In the formula is completely free, but not, since it has both a free and a bound occurrence.
- The logically equivalent formula can be obtained from the formula by bound renaming , in which both variables are free and completely free.
Web links
- Lecture notes "Logical Foundations of Computer Science" (PDF file; 1.07 MB)