First-Order Modal Semantics and Existence Predicate - Michalczenia, Patryk (Bulletin of the Section of Logic, 2022)
In the article we study the existence predicate \(ε\) in the context of semantics for first-order modal logic. For a formula \(φ\) we define \(φ^{ε}\) - the so called existence relativization. We point to a gap in the work of Fitting and Mendelsohn concerning the relationship between the truth of \(φ\) and \(φ^{ε}\) in classes of varying- and constant-domain models. We introduce operations on models which allow us to fill the gap and provide a more general perspective on the issue. As a result we obtain a series of theorems describing the logical connection between the notion of truth of a formula with the existence predicate in constant-domain models and the notion of truth of a formula without the existence predicate in varying-domain models.