A presupposition must be mutually known or assumed by the speaker and addressee for the utterance to be considered appropriate in context. It will generally remain a necessary assumption whether the utterance is placed in the form of an assertion, denial, or question, and can be associated with a specific lexical item or grammatical feature (presupposition trigger) in the utterance.

Bertrand Russell tries to solve this dilemma with two interpretations of the negated sentence:

For the first phrase, Russell would claim that it is false, whereas the second would be true according to him.

Hence, conditional sentences act as filters for presuppositions that are triggered by expressions in their consequent.

Some further factive predicates:

know; be sorry that; be proud that; be indifferent that; be glad that; be sad that.

Further iteratives: another time; to come back; restore; repeat; for the nth time.

Comparisons and contrasts may be marked by stress (or by other prosodic means), by particles like "too", or by comparatives constructions.

Questions often presuppose what the assertive part of the question presupposes, but interrogative parts might introduce further presuppositions. There are three different types of questions: yes/no questions, alternative questions and WH-questions.

But that presupposition, as stated, is completely trivial, given what we know about New York. Several million people had dinner in New York last night, and that in itself doesn't satisfy the presupposition of the sentence. What is needed for the sentence to be felicitous is really that somebody relevant to the interlocutors had dinner in New York last night, and that this has been mentioned in the previous discourse, or that this information can be recovered from it. Presupposition triggers that disallow accommodation are called anaphoric presupposition triggers.