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 which is called the hypothesis set
 * A WFF $\Phi \left({t}\right)$ attached to each non-root node $t$ of $T$.

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