Are Double Not Arrows vs. Exlusive ORs?

[commonlaw]

If I understand LGB correctly, Double Not Arrows ( ) are logically equivalent to the Exclusive Or (⊻).

For instance:
A B -A ⊻ -B
-A B A ⊻ -B
-A -B -A ⊻ B

If this is correct, I'm wondering if anyone has experimenting notating rules or inferences with Exclusive Ors instead of Double Not Arrows. The conditional nature of Double Not Arrows seems useful in certain contexts, namely making inferences and combination rules in the context of other conditionals. However, at certain times, especially with rules like -A -B, Double Not Arrows seem unnecessarily abstract compared to an expression like -A ⊻ B.

Consider these two logically equivalent chains of conditionals:
1. F -D -A -B C
2. F -D (-A ⊻ B) C

For (2.), I can immediately see on first glance that F results in A not being present or B being present, and that if either A is not present or B is present, then C will also be present. Whereas my brain stumbles to computer (1.) since there is an extra mental step involved in seeing through the negations on the page.

What do you think? Are there any pitfall to this technique?

[Adam Tyson]

In short, commonlaw, no - a double-not-arrow is NOT an exclusive or, because an exclusive or indicates that exactly one of the two variables must occur, whereas the double-not does not require that either condition occur, only that they cannot both occur together.

An exclusive or situation would be one where both versions of the double-not are in play, such as:

A B
and
A B

In this case, where exactly one must occur, if your diagrammatic choice covers that more efficiently for you and introduces no confusion, by all means use it! I'm not familiar with that symbology, but assuming it means that exactly one of the two variables occurs and the other does not, then it seems like a good way to go for those special cases. Our double-not-arrow is strictly for use when you have a sufficient condition that is positive and a necessary condition that is negative, such that you have three options:

A occurs and B does not
B occurs and A does not
NEITHER A nor B occurs

Good question, thanks for asking! Happy to clarify that one, as it is often the case that students assume incorrectly that one of the two must occur.