Topological product of modal logics with McKinsey axiom

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详细

We consider products of modal logics in topological semantics and prove that the topological product of S4.1 and S4 is the fusion of logics S4.1 and S4 plus one extra axiom. This is an example of a topological product of logics that is greater than the fusion but less than the semiproduct of the corresponding logics.

作者简介

A. Kudinov

Steklov Mathematical Institute of Russian Academy of Sciences

编辑信件的主要联系方式.
Email: kudinov.andrey@gmail.com
俄罗斯联邦, Moscow

参考

  1. Bezhanishvili G., Esakia L., Gabelaia D. Some results on modal axiomatization and definability for topological spaces // Studia Logica. 2005. Vol. 81 (3). P. 325–355.
  2. Bezhanishvili G., Gabelaia D., Lucero-Bryan J. Modal logics of metric spaces // The Review of Symbolic Logic. 2015. Vol. 8 (1). P. 178–191.
  3. Bezhanishvili G., Harding J. Modal logics of Stone spaces // Order. 2012. Vol. 29 (2). P. 271–292.
  4. Blackburn P., de Rijke M., Venema Y. Modal Logic. Cambridge University Press, 2002.
  5. Chagrov A., Zakharyaschev M. Modal Logic. Clarendon Press, Oxford, 1997.
  6. Gabbay D.M., Kurucz A., Wolter F., Zakharyaschev M. Many-dimensional modal logics: theory and applications / Studies in logic and the foundations of mathematics. Vol. 148. Elsevier, 2003.
  7. Gabelaia D. Modal Definability in Topology. Master thesis. ILLC, University of Amsterdam, 2001.
  8. Goldblatt R. The McKinsey axiom is not canonical // The Journal of Symbolic Logic. 1991. Vol. 56 (2. P. 54–562.
  9. Kremer P. The topological product of S4 and S5. Unpublished, 2011.
  10. Kudinov A., Shapirovsky I. Finite model property of pretransitive analogs of S5 // Russian Mathematical Surveys. 2012. Vol. 67 (4). P. 721–777.
  11. Kudinov A. Modal logic of some products of neighborhood frames // Advances in Modal Logic. 2012. P. 386–394.
  12. Kudinov A. On neighbourhood product of some Horn axiomatizable logics // Logic Journal of the IGPL. 2018. Vol. 26 (3). P. 316–338.
  13. Benthem van J., Bezhanishvili G., Cate B., Sarenac D. Multimodal logics of products of topologies // Studia Logica. 2006. Vol. 84. P. 369–392.
  14. Benthem van J., Bezhanishvili G. Modal logics of space / Handbook of spatial logics. Springer, 2007. P. 217–298.
  15. Дробышевич С.А., Одинцов С.П., Сперанский С.О. Введение в неклассические логики. Новосибирск: РИЦ НГУ, 2014.

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