Does and/or mean "and and or", or "and or or"? That is, if I say I am interested in A and/or B, do I mean I'm interested in A and B and I'm interested in A or B, or do I mean that I'm interested in A and B or I'm interested in A or B? (You may want to say that it means I'm interested in A and B and/or I'm interested in A or B; but in that case I repeat my question.)
Having reflected on it for a little while, I am convinced that the answer has to be that A and/or B must mean "A and B or A or B".
That is, if an entity A is claimed to have the property of being F and/or G, the claim amounts to saying that either (i) A has the property of being both F and G or (ii) A has the property of being either F or G. And to claim that F is a property of entities A and/or B is to claim that either (i) F holds for A and B or (ii) F holds for A or B.
However, in that case and/or is effectively identical in meaning with or, so it is at first rather hard to see why and/or exists at all. But I do have a guess.
The right theory of what or means in English is that it is in general inclusive but that sometimes the exclusive special case is conveyed as a conversational implicature. I'm going to study linguistics at either York or Edinburgh would often be taken to have the exclusive sense: since you typically go to a single university to take a single degree, and during the degree course you have no time to study elsewhere, a decision to choose York would normally exclude choosing Edinburgh as well. The exclusive sense is thus conveyed: one or the other of York and Edinburgh will be chosen, and if it is York it will not be Edinburgh, and if it is Edinburgh it will not be York. But of course if you think about it, someone who says she is choosing between those two universities does not commit herself for life to never studying at the other.
When the two alternatives exclude each other, then the exclusive meaning is the only one that makes sense. If you are asked whether you want to sit in the stalls or in the balcony, it's one or the other but not both, because you can only be in one place at one time. When they don't exclude each other, it's always understood that or allows for both: obviously someone whose ambition is to win either an Oscar or an Olympic medal wouldn't feel a failure if they won both. Winning both would satisfy the ambition in spades.
So my guess would be that and/or is a way of underlining the point that the or is to be understood in its inclusive sense rather than its exclusive sense. Sometimes you want to explicitly indicate "or more than one of the above", and and/or does that.
Take the first example of and/or in the Wall Street Journal corpus of 1987-1989 (a 44-million-word collection of random articles that linguists often use as a source for real-life examples because the Linguistic Data Consortium — the host for the giant Language Log servers — made it available in 1993 nice and cheap). The example (which actually happens to be a quotation from the Washington Post) is this:
Too many of his attitudes, claims and complaints are careless, conflicting, dubious, inaccurate, mean, petty, simplistic, superficial, uninformed and/or pointlessly biased.
I take it as obvious that if one hundred percent of the hapless man's attitudes, claims and complaints had all ten properties — every single one was careless and conflicting and dubious and inaccurate and mean and petty and simplistic and superficial and uninformed and pointlessly biased — then the quoted claim would be regarded as true, not false.
An or would have done the job here, but the and/or injects a (logically redundant) reminder that it may well be the case that more than one of the list of ten properties applies to the miserable individual in question.