Exclusive Disjunction (minimal logic)

Introduction Rule

$\frac{\begin{array}{cc}& [B{]}_i\\ & ⋮\\ A& \perp \end{array}}{A\succ \prec B}i$ OR $\frac{\begin{array}{cc}& [A{]}_i\\ & ⋮\\ B& \perp \end{array}}{A\succ \prec B}i$

Elimination Rule

$\frac{\begin{array}{ccc}& [A{]}_i& [B{]}_i\\ & ⋮& ⋮\\ A\succ \prec B& C& C\end{array}}{C}i$ OR $\frac{A\succ \prec BAB}{\perp }$