Definition:Labeled Tree for Propositional Logic/Attached

Definition

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

Let $t$ be a non-root node of $T$.

Let $\mathbf A$ be a WFF.

Then $\mathbf A$ is attached to $t$ if and only if $\mathbf A = \Phi \left({t}\right)$.

All the WFFs in the hypothesis set $\mathbf H$ are considered to be attached to the root node.

Also known as

The statement $\mathbf A$ is attached to $t$ can also be seen as:

• $\mathbf A$ occurs at $t$
• $\mathbf A$ is $t$.

Sources

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