Definition:Finished Branch of Propositional Tableau
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Definition
Let $T$ be a propositional tableau.
Let $\Gamma$ be a branch of $T$.
Then $\Gamma$ is finished if and only if:
- $(1): \quad \Gamma$ is not contradictory
- $(2): \quad$ Every non-basic WFF on $\Gamma$ is used at some node of $\Gamma$.
That is, $\Gamma$ is finished if and only if the set $\Delta$ of WFFs of propositional logic which occur along $\Gamma$ is a finished set.
Sources
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.10$: Completeness: Lemma $1.10.1$