First-Order Modal Semantics and Existence Predicate


  • Patryk Michalczenia University of Wroclaw, Institute of Philosophy, Koszarowa 3, 51-149 Wrocław, Poland image/svg+xml



first-order modal logic, constant-domain model, varying-domain model, existence predicate


In the article we study the existence predicate \(\varepsilon\) in the context of semantics for first-order modal logic. For a formula \(\varphi\) we define \(\varphi^{\varepsilon}\) - the so called existence relativization. We point to a gap in the work of Fitting and Mendelsohn concerning the relationship between the truth of \(\varphi\) and \(\varphi^{\varepsilon}\) 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.


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How to Cite

Michalczenia, P. (2022). First-Order Modal Semantics and Existence Predicate. Bulletin of the Section of Logic, 51(3), 317–327.



Research Article