On Certain Completeness Results for S4.2 Modal Logic and Its Applications in Modal Logics of Classes of Structures

Maciej A. Hałapacz

doi:10.18778/0138-0680.2026.16

On Certain Completeness Results for S4.2 Modal Logic and Its Applications in Modal Logics of Classes of Structures

Authors

Maciej A. Hałapacz University of Wrocław, Department of Logic and Methodology of Sciences, Wrocław, Poland Author https://orcid.org/0000-0001-8638-8488

DOI:

https://doi.org/10.18778/0138-0680.2026.16

Keywords:

control statements, modal logic S4.2, modal logics of classes of structures

Abstract

In this paper, we obtain new classes of Kripke frames complete for the modal logic S4.2, through the means of the so-called control statements. We provide applications of the theorem in the field of modal logics of classes of structures.

References

J. D. Hamkins, G. Leibman, B. Löwe, Structural connections between a forcing class and its modal logic, Israel Journal of Mathematics, vol. 207 (2015), pp. 617–651, DOI: https://doi.org/10.1007/s11856-015-1185-5.

J. D. Hamkins, B. Löwe, The modal logic of forcing, Transactions of the American Mathematical Society, vol. 360(4) (2008), pp. 1793–1817, DOI: https://doi.org/10.1090/S0002-9947-07-04297-3.

D. Saveliev, I. Shapirovsky, On modal logics of model-theoretic relations,Studia Logica, vol. 108 (2020), pp. 989–1017, DOI: https://doi.org/10.1007/s11225-019-09885-y.

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Published

2026-09-07

Issue

Early View

Section

Research Article

License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Hałapacz, Maciej A. 2026. “On Certain Completeness Results for S4.2 Modal Logic and Its Applications in Modal Logics of Classes of Structures”. Bulletin of the Section of Logic, September, 10 pp. https://doi.org/10.18778/0138-0680.2026.16.