The phrase "a rational relation" is correct and usable in written English.
It can be used in contexts discussing logical connections, mathematical relationships, or philosophical arguments.
Example: "In mathematics, a rational relation can be defined as a relationship between two variables that can be expressed as a ratio of integers."
Alternatives: "a logical connection" or "a reasonable relationship".
"The challenged regulations bear a rational relation to legitimate penological interests," Justice Anthony M. Kennedy wrote for seven members of the court.
Writing for himself and six others, Justice Kennedy said that while the regulations, particularly the two-year ban on visits, were "severe," they bore "a rational relation to legitimate penological interests" and did not fall below minimum constitutional standards.
In this system all parts of the painting bear a rational relation to each other and to the observer, for the observer's height and the distance he is to stand from the painting are controlled by the artist in laying out his perspective construction.
And the answer isn't simply "Because of a rational relation between the two".
Second, a model needs to be developed, describing a rational relation between the measure and the implementation effort.
We show how to modify the original set of defaults in order to obtain as output a rational relation.
Kraus, Lehmann, and Magidor proved that, for every preferential consequence relation that is probabilistically admissible,[5] there is a unique rational consequence relation * that minimally extends it (that is, that the intersection of all the rational consequence relations extending is also a rational consequence relation).
A preferential consequence relation that satisfies Rational Monotonicity is called a rational consequence relation.
We concluded that the provision was born of animosity toward the class of persons affected and further that it had no rational relation to a legitimate governmental purpose.
In Lawrence, Justice Kennedy observed that Romer "struck down class-based legislation directed at homosexuals" because "the provision was 'born of animosity toward the class of persons affected' and... had no rational relation to a legitimate government purpose".
For this purpose, we introduce the notion of stratification for a set of defaults, and prove that stratified sets are exactly those that induce a rational inference relation.
