# Definition:Tableau Confutation

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## Definition

Let $\mathbf H$ be a set of WFFs of propositional logic.

A **tableau confutation** of $\mathbf H$ is a propositional tableau $T$ with root $\mathbf H$ such that every branch of $T$ is contradictory.

## Also known as

When there is no danger of confusion, one often encounters **confutation** instead of **tableau confutation**.

If $\mathbf H = \left\{{\mathbf A}\right\}$ is a singleton set, then a **confutation** of $\mathbf H$ can be referred to as a **confutation of $\mathbf A$**.

## Also defined as

Some sources stipulate that a **tableau confutation** be finite.

That this does not lead to problems follows from Tableau Confutation contains Finite Tableau Confutation.

## Also see

## Sources

- 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.7$: Tableaus: Definition $1.7.4$