The union of all domains across worlds in a varying-domain model constitutes an ontological commitment to possibilia at the semantic level, as Lewis's distinction between inner and outer quantifiers establishes.
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ontological commitment(Used to derive that literal truth of 'a is F' entails existence of a)
The criterion by which acceptance of a sentence as literally true commits one to the existence of the objects referred to by singular terms in that sentence, provided the sentence cannot be paraphrased away.
possibilia(The ontological commitments that actualists seek to avoid)
Merely possible individuals — entities that exist in some possible world but not in the actual world
possible worlds(Leibniz's modal semantics, anticipating contemporary possible-worlds semantics)
Worlds that have existence in a tenuous sense; fictional worlds used to characterize the nature of possibles that are never actualized