RAS PresidiumДоклады Российской академии наук. Математика, информатика, процессы управления Doklady Mathematics

  • ISSN (Print) 2686-9543
  • ISSN (Online) 3034-5049

SEMIPRODUCTS, PRODUCTS, AND MODAL PREDICATE LOGICS: SOME EXAMPLES

PII
10.31857/S2686954323600325-1
DOI
10.31857/S2686954323600325
Publication type
Status
Published
Authors
Volume/ Edition
Volume 513 / Issue number 1
Pages
99-107
Abstract
We study two kinds of combined modal logics, semiproducts and products with S5, and their correlation with modal predicate logics. We obtain examples of propositional modal logics when these semiproducts or products are axiomatized in the minimal way (semiproduct- or product-matching with S5), as well as counterexamples for these properties. The fmp for (semi)products together with (semi)product-matching allow us to show decidability of corresponding 1-variable modal predicate logics.
Keywords
полупроизведения модальных логик произведения модальных логик предикатныe модальныe логики
Date of publication
01.03.2023
Year of publication
2023
Number of purchasers
0
Views
49

References

  1. 1. Segerberg K. “Two-dimensional modal logic,” Journal of Philosophical Logic. 1973. V. 2. № 1. P. 77–96.
  2. 2. Шехтман В.Б. “Двумерные модальные логики,” Математические заметки. 1978. Т. 23. С. 759–772.
  3. 3. Gabbay D., Kurucz A., Wolter F., Zakharyaschev M. Many-Dimensional Modal Logics: Theory and Applications. Elsevier, 2003.
  4. 4. Kurucz A. “Combining modal logics,” In: P. Blackburn, eds, Handbook of Modal Logic (Elsevier, 2008), p. 869–924.
  5. 5. Fischer-Servi G. “On modal logic with an intuitionistic base,” Studia Logica. 1977. V. 36. P. 141–149.
  6. 6. Gabbay D., Shehtman V. “Products of modal logics, Part 1,” Logic Journal of the IGPL. 1998. V. 6. № 1. P. 73–146.
  7. 7. Wolter F., Zakharyaschev M. “Decidable fragments of first-order modal logics,” The Journal of Symbolic Logic. 1999. V. 66. № 3. P. 1415–1438.
  8. 8. Rybakov M., Shkatov D. Undecidability of first-order modal and intuitionistic logics with two variables and one monadic predicate letter. Studia Logica. 2019. V. 107. № 4. P. 695–717.
  9. 9. Shehtman V., Shkatov D. “On one-variable fragments of modal predicate logics,” Proceedings of SYSMICS 2019 (University of Amsterdam, 2019), p. 129–132.
  10. 10. Shehtman V. “Simplicial semantics and one-variable fragments of modal predicate logics,” Topology, Algebra, and Categories in Logic, 2019, the book of abstracts (Nice, 2019), p. 172–173.
  11. 11. Shehtman V. “On Kripke completeness of modal predicate logics around quantified K5,” Annals of Pure and Applied Logic. 2023. V. 174. № 2. P. 103202.
  12. 12. Kracht M. Tools and Techniques in Modal Logic. Elsevier, 1999.
  13. 13. Shehtman V., Shkatov D. “Kripke (in)completeness of predicate modal logics with axioms of bounded alternativity,” Proceedings of FOMTL 2023 (ESSLLI, 2023), p. 26–29.
  14. 14. Gabbay D., Shehtman V., Skvortsov D. Quantification in Nonclassical Logic, Volume 1. Elsevier, 2009.
  15. 15. Shehtman V. “Segerberg squares of modal logics and theories of relation algebras,” In: S. Odintsov, ed., Larisa Maksimova on Implication, Interpolation, and Definability (Springer, 2018), p. 245–296.
  16. 16. Шехтман В.Б. “Бисимуляционные игры и локально табличные логики”. Успехи математических наук. 2016. T. 71. C. 185–186.
QR
Translate

Индексирование

Scopus

Scopus

Scopus

Crossref

Scopus

Higher Attestation Commission

At the Ministry of Education and Science of the Russian Federation

Scopus

Scientific Electronic Library