Theory-satisfiable Formula (Satisfiability Modulo Theory)

Definition

Theory-satisfiable Formula (Satisfiability Modulo Theory)

Let $\mathcal{T}$ be a theory over $\Sigma$. A $\Sigma$-formula $\phi$ is $\mathcal{T}$-satisfiable, or satisfiable modulo $\mathcal{T}$, if it is satisfiable in at least one [[Knowledge/Theory Interpretation (Satisfiability Modulo Theory)|$\mathcal{T}$-interpretation]]:

$$\exists I:I\models \mathcal{T}\wedge \phi \text{ is satisfiable in }I.$$