Definition:Labeled Tree for Propositional Logic

Definition
A labeled tree for propositional logic is a system containing:
 * A rooted tree $T$;
 * A countable set $\mathbf H$ of WFFs of propositional logic;
 * A WFF $\Phi \left({t}\right)$ attached to each non-root node $t$ of $T$.

Such a structure can be denoted $\left({T, \mathbf H, \Phi}\right)$.

Also denoted as
For ease of notation, one often writes $T$ in place of the more cumbersome $\left({T, \mathbf H, \Phi}\right)$ when this does not give rise to ambiguity.