- That has to be Jerry.
- That must be Jerry.
- That can't be Jerry.
DEONTIC modality is about what people think is good or right to do or not do. EPISTEMIC modality is basically about what we know. We indulge in it when we make judgements about what is, may, or cannot be true.
The Original Poster's example involves the epistemic use of HAVE TO:
Here the speaker is saying something along the lines of: from the evidence available I'm deducing that that's definitely Jerry. As far as epistemic modality is concerned, we could get more or less the same reading from the use of must:
Now there's two ways that we might want to negate this statement. We might want to say that it is not necessarily the case that that is Jerry. Technically we could say this by negating the HAVE TO sentence:
- That doesn't have to be Jerry!
However, this sounds pretty strange in English and we would probably only say this if we were contradicting someone who said That has to be Jerry. A more natural sentence would be something like That's not necessarily Jerry. Or even That might be Jerry. The last sentence doesn't have the same flavour, but actually boils down to the same thing.
On the other hand there is a completely different way to negate this sentence. We may want to reverse the judgement itself but keep the definitiveness involved in the original HAVE TO sentence. In other words we might want to say that that is necessarily not Jerry according to our evidence. When dealing with negative epistemic statements like this, we do not like to use mustn't to rule out a possibility. We have also already seen that doesn't have to means not necessarily - it doesn't mean necessarily not which is what we are after. We need to use can't or cannot here. So a negation of That has to be Jerry in terms of saying that it is necessarily not Jerry might be phrased thus:
When we move from epistemic modality to deontic modality however, the situation is not the same. Again we see a rough equivalence between MUST and HAVE TO:
- You have to leave the area.
- You must leave the area.
Again if we want to say that something is not necessary, we can use not have to:
- You don't have to leave the area.
But if we want to say that it's necessary that you don't do something we use mustn't:
- You mustn't leave the area.
Notice that we couldn't really achieve the same meaning using mustn't when dealing with epistemic modality. In that situation we used cannot or can't. We can use the same thing here too, although the sentence may be ambiguous:
- You can't leave the area.
We use HAVE TO and MUST for both deontic and epistemic necessity. However, to express a lack of necessity we use not have to. With epistemic judgements we are most likely to use can't to express that a proposition is necessarily not true. With deontic judgements we use mustn't to express that something necessarily not be done.
The example from the EFL site in the Original Poster's example is a bit strange for many readers. The reason is it uses mustn't for epistemic modality where we would expect can't. This does, having corresponded with some US speakers here, seem to be more specifically the case in GB English.
Hope this is helpful!
Edit note on epistemic mustn't
Notice that I said above that we do not "like to" use mustn't to rule out a possibility.
I didn't say that we can't. The Cambridge Grammar of the English Language Huddleston & Pullum et al 2002, state that although we sometimes use mustn't epistemically, it ...
... is quite rare and restricted (indeed unacceptable for many speakers): in negative contexts must and need are usually interpreted deontically. (pp. 180-1)
The thrust of this is that some speakers will just not give mustn't an epistemic reading, but that some other speakers do use it - although only in restricted environments.
Several writers here who speak varieties of US English have said that they believe this is much more acceptable in US English than it is in British English. It seems highly likely, therefore, that there is a difference in the acceptability of mustn't for epistemic modality between British and American Englishes.
Thank you to F.E. and JanusBahsJacquet for their input, and direction to relevant sources here.