Definition:Tableau Confutation

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 $\mathbf H = \set {\mathbf A}$ 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

• Tableau Confutation is Finished

Linguistic Note

The word tableau originates from the French language, where it means array, display, or table (in the sense of data presentation).

Hence the plural form of tableau is tableaux, although the US generally uses tableaus.

Tableaux is the preferred form on $\mathsf{Pr} \infty \mathsf{fWiki}$.

Sources

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