The projection problem.

The projection problem is to find the presuppositions of compound sentences given the presuppositions of their component sentences. Generally, the presuppositions of the compound sentences are just the presuppositions of the components, but this is not always the case. Presuppositions can be cancelled in various ways.

Some examples of projection of presuppositions:

S = not S1

It was not his dissertation that John lost.

Presupposition at S1: John lost something.

Presupposition at S: John lost something.

Here the presupposition projects to the compound sentence.

S = S1 or S2

Either it was his dissertation that John lost or he left it at home.

Presupposition at S1: John lost something.

Presupposition at S: John lost something.

Here the presupposition projects to the compound sentence.

S = modal(S1)

Maybe it was John who lost something.

Presupposition at S1: Someone lost something.

Presupposition at S: Someone lost something.

Here the presupposition projects to the compound sentence.

S = If S1 then S2.

If anyone lost his dissertation it was John who lost his dissertation.

Presupposition at S2: Someone lost his dissertation.

Presupposition at S: no projection.

If it was John who lost his dissertation there will be trouble.

Presupposition at S1: Someone lost his dissertation.

Presupposition at S: Someone lost his dissertation.

S = NP VP
VP = VP ADVP
ADVP = ADV S1

John cried before he finished his dissertation.

Entailment at S1: John finished his dissertation.

Presupposition at S: John finished his dissertation.

John died before he finished his dissertation.

Entailment at S1: John finished his dissertation.

Presupposition at S: No projection.

S = S1 and S2

It is possible that John wrote a dissertation and it is possible that John's dissertation is lost.

Presupposition at S2: John wrote a dissertation.

Presupposition at S: No projection.

Contextual effects.

S1: The king of France does not exist.

S2: The king of France is not in hiding.

Presupposition of S2 alone: There exists a king of France.

Presupposition of S1 and S2: No projection.

The presupposiiton conflicts with a proposition already placed in the conversational background.