"He can't have my phone number." ...has two meanings: 1. I refuse t give him my phone number. 2. It is highly unlikely (deduction) that he has my number. The meaning is taking from the context. By the way, it won't help if you classify modals into groups. It just clutters up your mind with useless information! Learn the modals one by one, exactly as I have shown you above. It is much quicker, and more natural.

Olga, Just in the present tense using negation? Here are a few. Most if not all of the modals can be manipulated to express deduction/speculation. May He may not be there....... About a 50% chance that he is not there. Must Jim is at work. He must not be sick....it is certain that Jim is not sick. Have to Colloquial use. It doesn't have to be him......maybe it is, maybe it isn't him. Can I have proof that Santa Claus can't exist..........it's impossible for him to exist He can't have my number, because I don't have a telephone.....it's impossibe Will The doorbell rang. Won't that be the mailman? ......high probability.

I think in the context of the expression from your link the speaker must be drawing a conclusion. Eliot has not called therefore he does not have my number. -> Eliot hasn't called. He can't have my number." The missing part of the sentence would be "Eliot has not called. He can't have my number in his possession." I can think of a situation that this expression might be natural: Lisa: I'm sure your friend Eliot has your phone number. Frank: I know he does NOT have my number! Lisa: Oh, I'm sure he does. Why do you think he doesn't? Frank: Eliot hasn't called. He CAN'T have my number.

As an exclamation, it can also mean, "I CAN'T believe he has my number!!! I tried SO hard to make sure he didn't get it!!!" I think it's tone of voice that makes the meaning clear in person. In writing, you'd need context clues to clarify which meaning.