On Finite Domains Based Slices in the Structure of Superintuitionistic Predicate Logics, Preview
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26.05.2023
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Abstract
The article presents a series of closely related papers that together make up a single piece of work, devoted to the description of a hierarchy of slices in the structure of superintuitionistic predicate logics and making probably the first attempt to transfer to the predicate case Hosoi's hierarchy of (finite) slices for the structure of superintuitionistic propositional logics.
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How to Cite
Skvortsov D. On Finite Domains Based Slices in the Structure of Superintuitionistic Predicate Logics, Preview // Logicheskie Issledovaniya / Logical Investigations. 2023. VOL. 29. № 1. C. 101-113.
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Section
Non-classical logics
Copyright (c) 2023 Dmitrij Skvortsov
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
Gabbay, 1972 – Gabbay, D.M. “Application of trees to intermediate logics”, Journal of Symbolic Logic, 1972, Vol. 37, pp. 135–138.
Gabbay et al., 2009 – Gabbay, D., Shehtman, V., Skvortsov, D. “Quantification in Nonclassical Logic”, Vol. 1, Studies in Logic and the Foundations of Mathematics, Vol. 153. Amsterdam: Elsevier Science Publisher, 2009. Sections 1.13, 1.15, 2.6.
Galatos et al., 2007 – Galatos, N., Jipsen, P., Kowalski, T., Ono, H. “Residuated Lattices: An Algebraic Glimpse at Substructural Logics”, Studies in Logic and the Foundations of Mathematics, Vol. 151. Amsterdam: Elsevier Science Publisher, 2007.
Gödel, 1933 – Gödel, K. “ Über Unabhängigkeitsbeweise im Aussagenkalkül”, Ergebnisse eines mathematischen Kolloquiums, 1933, Vol. 4, pp. 9–10.
Hosoi, 1967 – Hosoi, T. “On intermediate logics, I”, Journal of the Faculty of Science of the University of Tokyo, Sect. I, 1967, Vol. 14, No. 2, pp. 293–312.
Hosoi, 1969 – Hosoi, T. “On intermediate logics, II”, Journal of the Faculty of Science of the University of Tokyo, Sect. I, 1969, Vol. 16, No. 1, pp. 1–12.
Jankov, 1963 – Jankov, V.A. “The relationship between deducibility in the intuitionistic propositional calculus and finite implicational structures”, Dokl. Akad. Nauk SSSR, 1963, Vol. 151, pp. 1293–1294. (In Russian). English translation: Soviet Mathematics, Doklady, 1963, Vol. 4, pp. 1203–1204.
Jankov, 1969 – Jankov, V.A. “Conjunctively indecomposable formulas in propositional calculi”, Izvestiya Akademii Nauk SSSR, 1969, Vol. 33, pp. 13–38. (In Russian). English translation: Mathematics of the USSR–Izvestiya, 1969, Vol. 3, pp. 17–35.
Komori, 1975 – Komori, Y. “The finite model property of the intermediate logics of finite slices”, Journal of the Faculty of Science of the University of Tokyo, Sect. I, 1975, Vol. 22, pp. 117–120.
Maksimova, 1972 – Maksimova, L.L. “Pretabular superintuitionistic logics”, Algebra i Logika, 1972, Vol. 11, No. 5, pp. 558–570. (In Russian). English translation: “Pretabular superintuitionist logic”, Algebra and Logic, 1972, Vol. 11, No. 5, pp. 308–314.
Ono, 1972–1973 – Ono, H. “Some results on the intermediate logics”, Publications of RIMS, Kyoto University, 1972–1973, Vol. 8, pp. 117–130.
Skvortsov, in preparation – Skvortsov, D. “On propositional Jankov formulas, II”. In preparation.
Gabbay et al., 2009 – Gabbay, D., Shehtman, V., Skvortsov, D. “Quantification in Nonclassical Logic”, Vol. 1, Studies in Logic and the Foundations of Mathematics, Vol. 153. Amsterdam: Elsevier Science Publisher, 2009. Sections 1.13, 1.15, 2.6.
Galatos et al., 2007 – Galatos, N., Jipsen, P., Kowalski, T., Ono, H. “Residuated Lattices: An Algebraic Glimpse at Substructural Logics”, Studies in Logic and the Foundations of Mathematics, Vol. 151. Amsterdam: Elsevier Science Publisher, 2007.
Gödel, 1933 – Gödel, K. “ Über Unabhängigkeitsbeweise im Aussagenkalkül”, Ergebnisse eines mathematischen Kolloquiums, 1933, Vol. 4, pp. 9–10.
Hosoi, 1967 – Hosoi, T. “On intermediate logics, I”, Journal of the Faculty of Science of the University of Tokyo, Sect. I, 1967, Vol. 14, No. 2, pp. 293–312.
Hosoi, 1969 – Hosoi, T. “On intermediate logics, II”, Journal of the Faculty of Science of the University of Tokyo, Sect. I, 1969, Vol. 16, No. 1, pp. 1–12.
Jankov, 1963 – Jankov, V.A. “The relationship between deducibility in the intuitionistic propositional calculus and finite implicational structures”, Dokl. Akad. Nauk SSSR, 1963, Vol. 151, pp. 1293–1294. (In Russian). English translation: Soviet Mathematics, Doklady, 1963, Vol. 4, pp. 1203–1204.
Jankov, 1969 – Jankov, V.A. “Conjunctively indecomposable formulas in propositional calculi”, Izvestiya Akademii Nauk SSSR, 1969, Vol. 33, pp. 13–38. (In Russian). English translation: Mathematics of the USSR–Izvestiya, 1969, Vol. 3, pp. 17–35.
Komori, 1975 – Komori, Y. “The finite model property of the intermediate logics of finite slices”, Journal of the Faculty of Science of the University of Tokyo, Sect. I, 1975, Vol. 22, pp. 117–120.
Maksimova, 1972 – Maksimova, L.L. “Pretabular superintuitionistic logics”, Algebra i Logika, 1972, Vol. 11, No. 5, pp. 558–570. (In Russian). English translation: “Pretabular superintuitionist logic”, Algebra and Logic, 1972, Vol. 11, No. 5, pp. 308–314.
Ono, 1972–1973 – Ono, H. “Some results on the intermediate logics”, Publications of RIMS, Kyoto University, 1972–1973, Vol. 8, pp. 117–130.
Skvortsov, in preparation – Skvortsov, D. “On propositional Jankov formulas, II”. In preparation.