Definition:Labeled Tree for Propositional Logic/Along a Branch

Definition

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

Let $\Gamma$ be a branch of $T$.

Let $\mathbf A$ be a WFF that is attached to a node $t \in \Gamma$.

Then $\mathbf A$ occurs along $\Gamma$.

This includes the case where $\mathbf A \in \mathbf H$, that is, $\mathbf A$ is attached to the root node.

Also known as

That $\mathbf A$ occurs along $\Gamma$ can also be phrased:

$\mathbf A$ occurs on $\Gamma$.

Sources

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