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On Systems of Slices in the Structure of Superintuitionistic Predicate (or Propositional) Logics. I

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Abstract

The structure (i.e., the lattice) of superintuitionistic predicate logics is considered. An approach to classifying logics from the structure is discussed; this means that suitable partitions (via corresponding equivalence relations) are introduced. A few examples of such partitions are demonstrated (or mentioned).

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Notes

  1. The author (perhaps under the influence of his own personal preferences) is not inclined to object to the opinion of those specialists who believe that nonclassical logics (including superintuitionistic ones) can be an interesting (and even useful) tool for intellectual data analysis and reasoning.

  2. It is well-known that guarantees are spread by the not unknown policy, but would it really provide them?

REFERENCES

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  2. D. M. Gabbay, V. B. Shehtman, and D. P. Skvortsov, Quantification in Nonclassical Logic, Ed. by P. Suppes, Studies in Logic and the Foundations of Mathematics, Vol. 153 (Elsevier, Amsterdam, 2009), Sections 1.15, 2.6, and 2.15. https://doi.org/10.1016/s0049-237x(09)x0001-7

  3. H. Ono, “A study of intermediate predicate logics,” Publ. Res. Inst. Math. Sci. 8, 619–649 (1972). https://doi.org/10.2977/prims/1195192964

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  4. D. Skvortsov, “On the negative fragments of superintuitionistic predicate logics,” (2018).

  5. D. Skvortsov, “On finite domains based slices in the structure of superintuitionistic predicate logics, Preview,” Logical Invest. 29 (1), 101–113 (2023). https://doi.org/10.21146/2074-1472-2023-29-1-101-113

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ACKNOWLEDGMENTS

The author thanks V. Shekhtman, D. Shkatov, and anonymous reviewers for useful opinions that aid and facilitate improvement of the exposition.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333, Moscow, Russian Federation

    D. Skvortsov

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  1. D. Skvortsov
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Correspondence to D. Skvortsov.

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Dmitrij Skvortsov., born November 9, 1952. Candidate of Physics and Mathematics since 1980. Studied and defended his dissertation at the Moscow State University, Faculty of Mechanics and Mathematics. From 1978 to 2015/2021 he worked at the VINITI (All-Union/All-Russian Institute of Scientific and Technical Information); since 2016 he worked at the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences. Research interests: mathematical logic (author of about 100 publications).

Translated by E. Oborin

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Skvortsov, D. On Systems of Slices in the Structure of Superintuitionistic Predicate (or Propositional) Logics. I. Pattern Recognit. Image Anal. 33, 511–516 (2023). https://doi.org/10.1134/S1054661823030434

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  • DOI: https://doi.org/10.1134/S1054661823030434

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