First-Order Modal Semantics and Existence Predicate
DOI:
https://doi.org/10.18778/0138-0680.2022.07Keywords:
first-order modal logic, constant-domain model, varying-domain model, existence predicateAbstract
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.
References
M. Fitting, R. L. Mendelsohn, First-Order Modal Logic, vol. 277 of Synthese Library, Springer, Dordrecht (1998), DOI: https://doi.org/10.1007/978-94-011-5292-1
Google Scholar
DOI: https://doi.org/10.1007/978-94-011-5292-1
G. Frege, II.–On Concept and Object, Mind, vol. LX(238) (1951), pp. 168–180, DOI: https://doi.org/10.1093/mind/LX.238.168
Google Scholar
DOI: https://doi.org/10.1093/mind/LX.238.168
M. Kiteley, IV.–Is Existence a Predicate?, Mind, vol. LXXIII(291) (1964), pp. 364–373, DOI: https://doi.org/10.1093/mind/LXXIII.291.364
Google Scholar
DOI: https://doi.org/10.1093/mind/LXXIII.291.364
A. Meinong, On Object Theory, [in:] R. M. Chisholm (ed.), Realism and the Background of Phenomenology, The Free Press, Glencoe (1960), pp. 76–117.
Google Scholar
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
