Topological Semantics for da Costa Paraconsistent Logics \(C_\omega \) and \(C^{*}_\omega \)

  • Can Başkent
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 152)


In this work, we consider a well-known and well-studied system of paraconsistent logic which is due to Newton da Costa, and present a topological semantics for it.


Paraconsistent logic Topological semantics da Costa logics 

Mathematics Subject Classification (2000)

03B53 03B45 



This paper was partially written while I was visiting the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology at the University of St Andrews in the summer of 2011, and I am grateful for the help and encouragement of Graham Priest. The welcoming environment of St. Andrews facilitated the production of this paper. I am also very thankful for the tremendous help of the referee.


  1. 1.
    Arenas, F.G.: Alexandroff spaces. Acta Mathematica Universitatis Comenianae 68(1), 17–25 (1999)MathSciNetMATHGoogle Scholar
  2. 2.
    Awodey, S., Kishida, K.: Topology and modality: the topological interpretation of first-order modal logic. Rev. Symb. Logic 1(2), 146–166 (2008)MathSciNetMATHGoogle Scholar
  3. 3.
    Baaz, M.: Kripke-type semantics for da costa’s paraconsistent logic \(C_\omega \). Notre Dame J. Form. Logic 27(4), 523–527 (1986)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Başkent, C.: Some topological properties of paraconsistent models. Synthese 190(18), 4023–4040 (2013)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Béziau, J.-Y.: S5 is a paraconsistent logic and so is first-order classical logic. Log. Stud. 9(1) (2002)Google Scholar
  6. 6.
    Béziau, J.-Y.: Paraconsistent logic from a modal viewpoint. J. Appl. Logic 3(1), 7–14 (2005)CrossRefMATHGoogle Scholar
  7. 7.
    da Costa, N.C.A.: On the theory of inconsistent formal systems. Notre Dame J. Form. Logic 15(4), 497–510 (1974)CrossRefMATHGoogle Scholar
  8. 8.
    da Costa, N.C.A., Alves, E.H.: A semantical analysis of the calculi \(c_n\). Notre Dame J. Form. Logic 18(4), 621–630 (1977)CrossRefMATHGoogle Scholar
  9. 9.
    da Costa, N.C.A., Krause, D., Bueno, O.: Paraconsistent logics and paraconsistency. In: Jacquette, D. (ed.) Philosophy of Logic, vol. 5, pp. 655–781. Elsevier (2007)Google Scholar
  10. 10.
    Ferguson, T.M.: Notes on the model theory of demorgan logics. Notre Dame J. Form. Logic 53(1), 113–132 (2012)CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Fitting, M., Mendelsohn, R.: First-Order Modal Logic. Kluwer (1998)Google Scholar
  12. 12.
    Goldblatt, R.: Mathematical modal logic: a view of its evolution. In: Gabbay, D.M., Woods, J. (eds.) Handbook of History of Logic, vol. 6. Elsevier (2006)Google Scholar
  13. 13.
    Goodman, N.D.: The logic of contradiction. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 27(8–10), 119–126 (1981)CrossRefMATHGoogle Scholar
  14. 14.
    McKinsey, J.C.C.: On the syntactical construction of systems of modal logic. J. Symb. Logic 10(3), 83–94 (1945)CrossRefMathSciNetMATHGoogle Scholar
  15. 15.
    McKinsey, J.C.C., Tarski, A.: The algebra of topology. Ann. Math. 45(1), 141–191 (1944)CrossRefMathSciNetMATHGoogle Scholar
  16. 16.
    McKinsey, J.C.C., Tarski, A.: On closed elements in closure algebras. Ann. Math. 47(1), 122–162 (1946)CrossRefMathSciNetMATHGoogle Scholar
  17. 17.
    Mints, G.: A Short Introduction to Intuitionistic Logic. Kluwer (2000)Google Scholar
  18. 18.
    Mormann, T.: Heyting mereology as a framework for spatial reasoning. Axiomathes (2012)Google Scholar
  19. 19.
    Mortensen, C.: Topological seperation principles and logical theories. Synthese 125(1–2), 169–178 (2000)CrossRefMathSciNetMATHGoogle Scholar
  20. 20.
    Pratt-Hartman, I.E.: First-order mereotopology. In: Aiello, M., Pratt-Hartman, I.E., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 13–97. Springer (2007)Google Scholar
  21. 21.
    Priest, G.: First-order da costa logic. Stud. Logica 97, 183–198 (2011)CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Stell, J.G., Worboys, M.F.: The algebraic structure of sets of regions. In: Hirtle, S.C., Frank, A.U. (eds.) Spatial Information Theory. Lecture Notes in Computer Science, vol. 1329, pp. 163–174. COSIT 97. Springer (1997)Google Scholar
  23. 23.
    van Benthem, J., Bezhanishvili, G.: Modal logics of space. In: Aiello, M., Pratt-Hartman,I.E., van Benthem, J. (eds.) Handbook of Spatial Logics. Springer (2007)Google Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BathBathUK

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