... I'll just say that as far as I'm concerned 'may' = "may or may not". Maybe an example would help:
1) I can sing well.
For this to be a true statement I must have the ability to sing well. It doesn't mean that I will sing well, only that I have the ability.
2) I may sing well.
This statement is true whether I sing well or not. It simply denotes a possibility from 0% to 100% that I sing well, and doesn't mean I have the ability to sing well.
may = may or may not = illusory possibility = wishy-washy
can = has ability = finite state.
Precisely my point. I don't believe I've ever heard "can or can not" used as a proxy for "can."
Perhaps it's mostly a matter of style, but I believe there is enough in ordinary dictionaries to support dablueman's interpretation. If "can" serves your purposes, I think it's a total no-brainer to use that instead of "may."
If may = may or may not, then by substitution:
.... :
1 = 1 or not 1
Well, that's sort of right. "May" means "might" = has a probability of A where 0 < A < 1.
So, really, "may" implicitly includes "may not" which also has a probability greater than zero and less than one. So, perhaps a more mathematically correct way to say "may or may not" would be "may and may not".
Thus, to say that my car may be blue and that my car may and may not be blue are the same thing. I'm saying that my car has some probability A (where 0 < A < 1) of being blue and a complementary probability of 1-A of not being blue. I think that's mathematically sound.
I'll admit that "may and/or may not" is so lacking in providing useful information that some might wonder why that interpretation makes any sense at all -- why even have the phrase in our language? I have 2 answers to that, and I think only one of them makes sense in patents.
The first is to negate a prior assertion. Suppose someone tells you that Jim's car is blue. If someone else says that Jim's car may be blue, that suggests that it also may not be blue, thereby negating the prior assertion without asserting its opposite.
The second is to describe a contingency. Jim will bring his car in for body work and Jim's car may be blue. If so, here's what we're going to do. In many human-machine interface (HMI) technologies, the stochastic process of user interaction is often described using "may" and the responsive actions of the machine are typically deterministic and generally not described using "may" (in my work, anyway).
As for the chemical group hypothetical(s), I don't know enough about that to comment. To the extent "may not" is an insane interpretation due to some inherency of the elements mentioned in the phrase, it's not a fair example. For example, to say that human beings may not have human DNA is unreasonable, but not because of the meaning of "may".
Regards.