Definition:Falsifiable/Boolean Interpretations
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Definition
Let $\mathbf A$ be a WFF of propositional logic.
$\mathbf A$ is called falsifiable (for boolean interpretations) if and only if:
- $\map v {\mathbf A} = \F$
for some boolean interpretation $v$ for $\mathbf A$.
In terms of validity, this can be rendered:
- $v \not\models_{\mathrm{BI}} \mathbf A$
that is, $\mathbf A$ is invalid in the boolean interpretation $v$ of $\mathbf A$.
Also see
- Definition:Valid (Boolean Interpretation)
- Definition:Satisfiable (Boolean Interpretations)
- Definition:Unsatisfiable (Boolean Interpretations)
Sources
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.5$: Definition $2.38$