In pragmatics Presupposition is what the speaker assumes to be the case prior to making an utterance. Entailment, which is not a pragmatic concept, is what logically follows from what is asserted in the utterance. Speakers have presuppositions while sentences, not speakers, have entailments. Take a look at the example below:
Jane's brother bought two apartments.
This sentence presupposes that Jane exists and that she has a brother. The speaker may also hold the more specific presupposition that she has only a brother and her brother has a lot of money. All these presuppositions are held by the speaker and all of them can be wrong.
In pragmatics entailment is the relationship between two sentences where the truth of one (A) requires the truth of the other (B). For example, the sentence (A) The president was assassinated. entails (B) The president is dead.
Presupposition
The concept of presupposition is often treated as the relationship between two propositions. In the case below, we have a sentence that contains a proposition (p) and another proposition (q), which is easily presupposed by any listener. However, the speaker can produce a sentence by denying the proposition (p), obtaining as a result the same presupposition (q).
Debora's cat is cute. (p)
Debora has a cat. (q)
When I say that Debora' s cat is cute, this sentence presupposes that Debora has a cat. In
Debora' s cat is not cute. (NOT p)
Types of Presupposition