Full Idea
The most robust tests for presupposition are the projection tests. If s presupposes p, then Žs does too. If s1 presupposes p, then 'if s1 then s2' presupposes p. If s1 presupposes p, then 's1 and s2' presupposes p. If s presupposes p, then 's?' does too.
Gist of Idea
The best tests for presupposition are projecting it to negation, conditional, conjunction, questions
Source
Ofra Magidor (Category Mistakes [2013], 5.3.1.3)
Book Reference
Magidor,Ofra: 'Category Mistakes' [OUP 2013], p.120
A Reaction
[compressed] She also discusses quantifiers. In other words, the presupposition remains stable through various transformations of the underlying proposition.