Question

1. He is a doctor of this hospital.
2. He is the doctor of this hospital.
3. He is the only doctor of this hospital.

[Does #2 mean #3? Is #2 logical? I think #1 is a common expression. Is that right?]

4. She is the principal of this school.
5. She is a principal of this school.
6. She is the only principal of this schoo.
[We can use #4, right? How about #5? #5 means that there are sevral prnicipals and she is one of them. Is this logical? Does #4 mean #6? #4 seems to be a common expression. Right?]

Answer 1

2 and 3 mean the same thing. We might say "at this hospital", not "of", but they do mean the same thing. 1 means he is one of potentially more than one doctor at the hospital.

#4 is best. I don't know how schools are administered in your country, but, in the USA, there is only one principal per school. There may be vice-principals in large schools, but only one principal.