Record link: 
http://hdl.handle.net/20.500.12708/230336
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Title: 
Skolemization and Decidability of the Bernays–Schönfinkel Class in Gödel Logics
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Citation: 
Baaz, M., Gamsakhurdia, M., & Lolić, A. (2026). Skolemization and Decidability of the Bernays–Schönfinkel Class in Gödel Logics. In 2026 IEEE 56th International Symposium on  Multiple-Valued Logic (ISMVL 2026) (pp. 25–30). IEEE. https://doi.org/10.1109/ISMVL68998.2026.00014
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Publisher DOI: 
10.1109/ISMVL68998.2026.00014
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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: 
2026 IEEE 56th International Symposium on Multiple-Valued Logic (ISMVL 2026) 
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ISBN: 
979-8-3315-5956-4
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DOI of the book: 
10.1109/ISMVL68998.2026
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Date (published): 
11-Jun-2026
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Event name: 
56th International Symposium on Multiple-Valued Logic (ISMVL 2026) 
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Event date: 
19-May-2026 - 21-May-2026
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Event place: 
Sendai, Japan
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Number of Pages: 
6
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Publisher: 
IEEE
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Peer reviewed: 
Yes
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Keywords: 
Bernays-Schönfinkel class; Decidability; Gödel Logics; Skolemization
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Abstract: 
In 1928, Bernays and Schönfinkel proved the decidability of prenex sentences whose matrices contain no function symbols, now known as the Bernays-Schönfinkel (BS) class. We investigate the decidability of the BS class for all Gödel logics. Our validity argument relies on the fact that Skolemization works for prenex Gödel logics, while 1-satisfiability follows from the structural properties of prenex formulas. We show that validity and 1-satisfiability for the BS class are decidable in every Gödel logic, and that these properties persist across all infinite Gödel logics.
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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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