First-order modal logic
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monodic fragments
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∀yφ → ∀y∀xφ,
as we show by constructing a counter-model.