Definition:Propositional Tableau/Graphical Representation

Definition
The conditions by which a propositional tableau may be identified, respectively constructed, can be graphically represented like so:


 * $\begin{xy}\xymatrix @R=1em @C=3em{

\ar@{.}[d] & \ar@{.}[d] & \ar@{.}[d] & \ar@{.}[d] \\ *++{\neg \neg \mathbf A} \ar@{.}[d] & *++{\mathbf A \land \mathbf B} \ar@{.}[d] & *++{\neg \left({\mathbf A \lor \mathbf B}\right)} \ar@{.}[d] & *++{\neg \left({\mathbf A \implies \mathbf B}\right)} \ar@{.}[d] \\ *++{t} \ar@{-}[d] & *++{t} \ar@{-}[d] & *++{t} \ar@{-}[d] & *++{t} \ar@{-}[d] \\ \mathbf A & \mathbf A \ar@{=}[d] & \neg \mathbf A \ar@{=}[d] & \mathbf A \ar@{=}[d] \\ & \mathbf B & \neg \mathbf B & \neg \mathbf B \\ \boxed{\neg\neg} & \boxed \land & \boxed{\neg\lor} & \boxed{\neg\implies} }\end{xy}$