@article{Michalczenia_2022, title={First-Order Modal Semantics and Existence Predicate}, volume={51}, url={https://czasopisma.uni.lodz.pl/bulletin/article/view/12357}, DOI={10.18778/0138-0680.2022.07}, abstractNote={<p>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 <em>existence relativization</em>. 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.</p>}, number={3}, journal={Bulletin of the Section of Logic}, author={Michalczenia, Patryk}, year={2022}, month={Jul.}, pages={317–327} }