# Definition:Marked Leaf

(Redirected from Definition:Unmarked Leaf)

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## Definition

Let $T$ be a semantic tableau.

Let $t$ be a leaf of $T$.

Then $t$ is **marked** iff it has occurred in **Step 3** of the Semantic Tableau Algorithm.

Otherwise, it is called **unmarked**.

### Marked Closed Leaf

A marked leaf $t$ of $T$ is **marked closed** iff its label $U \left({t}\right)$ contains a complementary pair.

This can be designated by adding to $t$ a second label $\times$.

### Marked Open Leaf

A marked leaf $t$ of $T$ is **marked open** iff its label $U \left({t}\right)$ does not contain a complementary pair.

This can be designated by adding to $t$ a second label $\odot$.

## Sources

- 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): $\S 2.6.2$: Algorithm $2.64$