Definition:Propositional Tableau/Construction/Infinite
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Definition
An infinite labeled tree $\left({T, \mathbf H, \Phi}\right)$ is a propositional tableau if and only if:
- There exists an exhausting sequence of sets $\left({T_n}\right)_{n \in \N}$ of $T$ such that for all $n \in \N$:
- $\left({T_n, \mathbf H, \Phi \restriction_{T_n}}\right)$
- is a finite propositional tableau, where $\Phi \restriction_{T_n}$ denotes the restriction of $\Phi$ to $T_n$.
Sources
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.7$: Tableaus: Definition $1.7.3$