Record link: 
http://hdl.handle.net/20.500.12708/221747
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Title: 
An Analytic Representation of the Semantics of First-Order S5
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Citation: 
Baaz, M., Gamsakhurdia, M., & Lolić, A. (2025). An Analytic Representation of the Semantics of First-Order S5. In R. Thiemann & C. Weidenbach (Eds.), Frontiers of Combining Systems : 15th International Symposium, FroCoS 2025, Reykjavik, Iceland, September 29 – October 1, 2025, Proceedings (pp. 63–79). Springer. https://doi.org/10.1007/978-3-032-04167-8_4
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Publisher DOI: 
10.1007/978-3-032-04167-8_4
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Baaz, Matthias 
Gamsakhurdia, Mariami 
Lolić, Anela 
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Organisational Unit: 
E104-02 - Forschungsbereich Computational Logic 
E192-05 - Forschungsbereich Theory and Logic 
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Published in: 
Frontiers of Combining Systems : 15th International Symposium, FroCoS 2025, Reykjavik, Iceland, September 29 – October 1, 2025, Proceedings 
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ISBN: 
978-3-032-04167-8
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Volume: 
15979
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DOI of the book: 
10.1007/978-3-032-04167-8
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Date (published): 
15-Sep-2025
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Event name: 
15th International Symposium on Frontiers of Combining Systems (FroCoS 2025) 
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Event date: 
29-Sep- 225 - 1-Oct- 225
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Event place: 
Reykjavik, Iceland
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Number of Pages: 
17
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Publisher: 
Springer, Cham
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Peer reviewed: 
Yes
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Keywords: 
Cut elimination; Herbrand’s theorem; Interpolation; Modal S5; Prenex fragment; Two-sorted logic
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Abstract: 
One of the most fascinating examples of the failure of Beth’s definability theorem and, consequently, of Craig’s interpolation theorem, is quantified S5. In this paper, we intend to establish the interpolation property for fragments of quantified S5 using a formulation of the semantics of quantified S5 as an analytic calculus in its own right. This is especially straightforward for S5, because necessity (possibility) in S5 means for all worlds (there exists a world), and we have simply to extend every predicate by a world position (worlds and objects are to be considered as separate entities).
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Research Areas: 
Logic and Computation: 100%
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Science Branch: 
1020 - Informatik: 5%
1010 - Mathematik: 95%
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Appears in Collections:
Conference Paper

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