The Finite Embeddability Property for Topological Quasi-Boolean Algebra 5

  • Zhe LinEmail author
  • Mihir Kumar Chakraborty
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11600)


In this paper we study some basic algebraic structures of rough algebras. We proved that the class of topological quasi-Boolean algebra 5s (tqBa5s) has the finite embeddability property (FEP). Further we also extend this result to some related classes of algebras.


  1. 1.
    Banerjee, M., Chakraborty, M.: Rough algebra. Bull. Pol. Acad. Sci. (Math.) 41(4), 293–297 (1993)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Banerjee, M., Chakraborty, M.: Rough sets through algebraic logic. Fundamenta Informaticae 28(3–4), 211–221 (1996)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)CrossRefGoogle Scholar
  4. 4.
    Rasiowa, H.: An Algebraic Approach to Non-Classical Logics. North-Holland PublishingGoogle Scholar
  5. 5.
    Banerjee, M.: Rough sets and 3-valued lukasiewicz logic. Fundamenta Informatica 31, 213–220 (1997)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Saha, A., Sen, J., Chakraborty, M.: Algebraic structures in the vicinity of pre-rough algebra and their logics. Inf. Sci. 282, 296–320 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Saha, A., Sen, J., Chakraborty, M.: Algebraic structures in the vicinity of pre-rough algebra and their logics II. Inf. Sci. 333, 44–60 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Block, W., van Alten, C.: The finite embeddability property for residuated lattices pocrims and bckcalgebras. Algebra Universalis 48, 253–271 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Block, W., van Alten, C.: On the finite embeddability property for residuated ordered groupoids. Trans. Am. Math. Soc. 357(10), 4141–4157 (2004)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Farulewski, M.: Finite embeddability property for residuated groupoids. Rep. Math. Logic 43, 25–42 (2008)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Buszkowski, W.: Interpolation and FEP for logic of residuated algebras. Logic J. IGPL 19(3), 437–454 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zhe, L.: Non-associative Lambek calculus with modalities: interpolation, complexity and FEP Zhe Lin. Logic J. IGPL 22(3), 494–512 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lin, Z., Chakraborty, M.K., Ma, M.: Decidability in pre-rough algebras: extended abstract. In: Nguyen, H.S., Ha, Q.-T., Li, T., Przybyła-Kasperek, M. (eds.) IJCRS 2018. LNCS (LNAI), vol. 11103, pp. 511–521. Springer, Cham (2018). Scholar
  14. 14.
    Chakraborty, M., Sen, J.: A study of interconnections between rough and 3-valued lukasiewicz logics. Fundam. Inf. 51, 311–324 (2002)zbMATHGoogle Scholar
  15. 15.
    van Benthem, J., Bezhanishvili, G.: Modal logic of spaces. In: Aliello, M., Pratt-Hartmann, I., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 217–298. Springer, Dordrecht (2007). Scholar
  16. 16.
    Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Springer (2007)Google Scholar
  17. 17.
    Lambek, J.: On the calculus of syntactic types. Am. Math. Soc. XII, C178 (1961)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Logic and CognitionSun Yat-sen UniversityGuangzhouChina
  2. 2.School of Cognitive ScienceJadavpur UniversityKolkataIndia

Personalised recommendations