Model (First-Order Logic)

first-order-logic

Definition

Model (First-Order Logic)

A model is a semantic object that makes something true. What counts as a model depends on what is being satisfied:

What	Model is	When
Sentence $\phi$	a structure $\mathcal{M}$	$\mathcal{M}\models \phi$
Formula $\phi$	an interpretation $(\mathcal{M},\ell )$	$(\mathcal{M},\ell )\models \phi$
Theory $\Gamma$	a structure $\mathcal{M}$	$\mathcal{M}\models \phi$ for all $\phi \in \Gamma$