Definition:Labeled Tree for Propositional Logic/Hypothesis Set

Definition

Let $\struct {T, \mathbf H, \Phi}$ 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.

Sources

• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.7$: Tableaus