Definition:Labeled Tree for Propositional Logic/Hypothesis Set

Definition
Let $\left({T, \mathbf H, \Phi}\right)$ be a labeled tree for propositional logic.

The countable set $\mathbf H$ of WFFs of propositional logic is called the hypothesis set.

The elements of $\mathbf H$ are known as hypothesis WFFs.

The hypothesis set $\mathbf H$ is considered to be attached to the root node of $T$.

Also known as
$\mathbf H$ is also called the set of premises.

In the context of propositional tableaus, it is also called the root.