Commutativity of Quantifiers in Varying-Domain Kripke Models
Robert Goldblatt and Ian Hodkinson
A possible-worlds semantics is defined that validates the main axioms of Kripke's original system
for first-order modal logic over varying-domain structures. The novelty of this semantics is that
it does not validate the commutative quantification schema
∀x ∀y &phi &rarr ∀y ∀x &phi,
as we show by constructing a counter-model.