I would like to express formally the following disjunction:
Either A is the case or B is the case or C is the case and only one among A, B and C is the case. In other words: at least one among A, B and C is the case and only one of them is the case.
How do you express this formally? Is this equivalent to an exclusive disjunction?
If you are thinking of doing $$A \ XOR \ B \ XOR \ C$$
... no, that doesn't work: a generalized XOR is true iff an odd number of its terms are true, so this expression would also be true if all of $A$, $B$, and $C$ are true.
I think your best option is just to go with something like
$$(A \land \neg B \land \neg C) \lor (\neg A \land B \land \neg C) \lor (\neg A \land \neg B \land C)$$