Lakoff, p. 148

“Let us consider a simple example of a presupposition.

(a) I regret that Harry left.

(b) I don’t regret that Harry left.

(c) Harry left.

Normally, the speaker who says (a) or its negation, (b), is taking (c) for

granted. In the 1960s there were two alternatives available for trying to

account for this phenomenon.

LOGICAL PRESUPPOSITION: Both (a) and its negation, (b), logically entail (c).

Logical entailment is defined in terms of truth in the world. Thus, when-

ever (a) or (b) is true in the world, (c) must be true in the world. This

leads to problems for sentences like

(d) I don’t regret that Harry left-in fact, he didn’t leave at all.

If the theory of logical presupposition were correct, then (d) should be a

logical contradiction, since the first half entails the truth of (c) and the sec-

ond half denies (c). But since (d) is not a logical contradiction, the theory

of logical presupposition cannot hold for such cases.”

Not so fast. It depends upon how to interpret (b) since sentences like (b) ar ambiguos in english. This is so becus they use a frase similar to “I don’t [verb]”. If we are to be mor cleer, then here ar the two interpretations of (b):

(b’). There is a person, x, and there is a person, y, such that x = me and y = Harry, and y left, and it is not the case that x regrets that y left.

∃x∃y(x=m)&(y=h)&Ly&~Rx(Ly)

(b”). It is not the case that, there is a person, x, and there is a person, y, such that x = me and y = Harry, and y left, and x regret that y left.

~∃x∃y(x=m)&(y=h)&Ly&Rx(Ly)

Thees two ar not equivalnt. (b’) does indeed imply (c) but (b”) does not imply (c).

Using interpretation (b”), (d) does not seem to be a contradiction, but using (b’), it is a contradiction

becus it implys both (c) and ~(c).