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Explicit basis for admissible rules in K-saturated tabular logics

  • Vitalii V. Rimatskii
Published/Copyright: April 11, 2023

Abstract

We construct an explicit finite basis for admissible rules in K-saturated tabular logics that extend the logic Grz.


Note

Originally published in Diskretnaya Matematika (2022) 34,№1, 126–140 (in Russian).


Funding statement: Supported by the Russian Foundation for Basic Research and the Krasnoyarsk Regional Science Foundation (grant no. 18-41-240005).

References

[1] Lorenzen P., Einfung in Operative Logik und Mathematik, Berlin–Göttingen–Heidelberg, 1955, 816 pp.10.1007/978-3-662-01539-1Search in Google Scholar

[2] Friedman H., “One hundred and two problems in mathematical logic”, J. Symb. Logic, 40:3 (1975), 113–13010.2307/2271891Search in Google Scholar

[3] Rybakov V. V., “A criterion for admissibility of rules in the model system S4 and the intuitionistic logic 𝐻”, Algebra and Logic, 23:5 (1984), 369–384.10.1007/BF01982031Search in Google Scholar

[4] Rybakov V. V., Admissibility of Logical Inference Rules, Studies in Logic and Found. of Math., V.136., Elsevier Sci. Publ, New-York–Amsterdam, 1997, 616 pp.Search in Google Scholar

[5] Rimatskii V. V., “Bases of admissible inference rules for table modal logics of depth 2”, Algebra and Logic, 35:5 (1996), 344–349.10.1007/BF02367359Search in Google Scholar

[6] Rimatskii V. V., “Bases of admissible rules for K-saturated logics”, Algebra and Logic, 47:6 (2008), 420–425.10.1007/s10469-008-9033-xSearch in Google Scholar

[7] Rimatskii V. V., Lukina O.V., “Explicit basis of admissible rules for the finding of tabular logic”, Vestnik Krasnoyarsk. gos. un-ta, 2006,№1, 68–71 (in Russian).Search in Google Scholar

[8] Rimatskii V. V., “Finite bases with respect to admissibility for modal logics of width 2”, Algebra and Logic, 38:4 (1999), 436–455.10.1007/BF02671729Search in Google Scholar

[9] Rimatskii V. V., Kiyatkin V. R., “The independent bases for admissible inference rules of pretabular logics and its extensions”, Sib. Electron. Mathem. Rep., 10 (2003), 79–89 (in Russian).Search in Google Scholar

[10] Rybakov V. V., Terziler M., Rimatskiy V. V., “Basis in semi-redused form for the admissible rules of the intuitionistic logic IPC”, Math. Logic Quarterly, 46:2 (2000), 207–218.10.1002/(SICI)1521-3870(200005)46:2<207::AID-MALQ207>3.0.CO;2-ESearch in Google Scholar

[11] Iemhoff R., “On the admissible rules of intuitionistic propositional logic”, J. Symb. Logic, 66:2 (2001), 281–294.10.2307/2694922Search in Google Scholar

[12] Rybakov V. V., “Construction of an explicit basis for rules admissible in modal system S4”, Math. LogicQuarterly, 47:4 (2001), 441–451.10.1002/1521-3870(200111)47:4<441::AID-MALQ441>3.0.CO;2-JSearch in Google Scholar

[13] Rimatskii V. V., “Explicit basis of admissible rules for the finding of finite width”, Zhurnal SFU, Ser. matem. i fizika, 2008,№1, 85–93 (in Russian).Search in Google Scholar

[14] Rybakov V. V., Terziler M., Genzer C., “An essay on unification and inference rules for modal logic”, Bull. Sect. Log., 28:3 (1999), 145–157.Search in Google Scholar

Received: 2021-10-02
Published Online: 2023-04-11
Published in Print: 2023-03-28

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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