What are the semantic tableaux tree rules for exclusive disjunction? These are the rules for the traditional PL connectives:

How do I resolve the tree when there is in a exclusive disjunction (⊻) in an argument?
 A: Figuring that this is probably a homework question, I'll just give you a hint:
Just investigate the cases where an exclusive disjunction is true/false:

*

*$\alpha ⊻ \beta$ is true iff exactly one of them is true, that is

*

*either $\alpha$ is true and $\beta$ is false

*or $\alpha$ is false and $\beta$ is true.



*$\alpha ⊻ \beta$ is false iff they are both true or both false, that is

*

*either $\alpha$ is true and $\beta$ is true

*or $\alpha$ is false and $\beta$ is false.



Knowing that in a tableau tree, branching represents an "or" between conditions, vertical stacking corresponds to "and", and falsity is expressed by negating the formula, you can translate these truth conditions directly into a taleau rule.
As a further hint, note that exclusive disjunction is the negation of the biconditional: $\alpha ⊻ \beta$ is logically equivalent to $\neg(\alpha \leftrightarrow \beta)$, and $\neg(\alpha ⊻ \beta) \equiv \alpha \leftrightarrow \beta$, so the rule pairs will be the exact "opposite" of each other. That should make it pretty easy for you to figure it out now.
