previous up next
Go backward to
Go up to Top
Go forward to Minimum and Maximum Function
RISC-Linz logo

Minimum and Maximum Quantifier

Definition: If x is a variable and F is a formula, then the following are terms with bound variable x:

minx F
maxx F

The value of the first term is the smallest value of x such that F holds; the value of the second term is the largest such value:

minx F := such x: F /\  (forall y: F[x <- y] => x <= y);
maxx F := such x: F /\  (forall y: F[x <- y] => x >= y).

Quantifiers for every domain with a binary predicate <= .

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

previous up next