Describes a first-order Kripke model for modal logic in which the domain of any possible world $w$ is a subset of any world $w^{\prime }$ accessible from $w$, i.e., in which the domains are monotonic. Formally, where $D_w$ represents the domain of individuals of a world $w$, this is represented by the semantic condition:

If $wR{w}^{\prime }$ then $D_w\subseteq D_{w^{\prime }}.$

For normal first-order modal logics, the semantic condition of increasing domains corresponds to the validity of the converse Barcan formula

• • $\square \forall x\phi \left(x\right)\to \forall x\square \phi \left(x\right)$

Increasing domain models are special cases of variable domain models.