A presupposition denial is a noncontradictory negation of a presupposition in a clause by an assertion in another clause.
In the utterance John doesn’t regret doing a useless Ph.D., because, in fact, he never did do one, the presupposition "John did a useless Ph.D." is denied by the second clause.
Levinson, Stephen C. 1983.Pragmatics. Cambridge, England: Cambridge University.