Suppose I have something like:
$A\backslash B\backslash C$
Does that mean $(A\backslash B)\backslash C$ ,elements in A, but neither in B nor C
Or does it mean $A\backslash(B\backslash C)$ ,elements in A not in B, unless they are also in C
As always, creating such a construction is a bad idea, as it is always best to state what you mean clearly, but in what order would chained set complements be interpreted?
I'm not sure, but it would make perfect sense to treat the relative complement operator as left-associative.
When we say $A - B - C$ for numbers, we never expect it to mean $A - (B - C)$, unless specifically written that way.
If you're defining it yourself, say in a programming language, then of course it depends on your intention, which should ideally reflect in your grammar.
<compl>$ \ \rightarrow$ <set> <compl-chain>
<compl-chain> $ \ \rightarrow$ \ <set> | \ <set> <compl-chain>
The parse tree for this grammar would be leaning to the right, so the most intuitive evaluation would be right-associative.