Definition:Tableau Proof (Propositional Tableaux)/Proof System
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Proof System
Tableau proofs form a proof system $\mathrm{PT}$ for the language of propositional logic $\LL_0$.
It consists solely of axioms, in the following way:
- A WFF $\mathbf A$ is a $\mathrm{PT}$-axiom if and only if there exists a tableau proof of $\mathbf A$.
Likewise, we can define the notion of provable consequence for $\mathrm{PT}$:
- A WFF $\mathbf A$ is a $\mathrm{PT}$-provable consequence of a collection of WFFs $\mathbf H$ if there exists a tableau proof of $\mathbf A$ from $\mathbf H$.
Although formally $\mathrm{PT}$ has no rules of inference, the rules for the definition of propositional tableaux can informally be regarded as such.
Sources
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.7$: Tableaus