Definition:Satisfiable/Boolean Interpretations

Definition

Let $\mathbf A$ be a WFF of propositional logic.

$\mathbf A$ is called satisfiable (for boolean interpretations) if and only if:

$\map v {\mathbf A} = \T$

for some boolean interpretation $v$ for $\mathbf A$.

In terms of validity, this can be rendered:

$v \models_{\mathrm{BI}} \mathbf A$

that is, $\mathbf A$ is valid in the boolean interpretation $v$ of $\mathbf A$.

Also see

• Definition:Valid (Boolean Interpretation)
• Definition:Tautology (Boolean Interpretations)
• Definition:Unsatisfiable (Boolean Interpretations)

Sources

• 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.4.1$: The meaning of logical connectives: Exercise $1.8: \ 5$
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.5$: Definition $2.38$