On the Usefulness of Paraconsistent Logic

  • Newton C.A. da Costa
  • Jean-Yves Béziau
  • Otávio Bueno
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 2)


In this paper, we examine some intuitive motivations to develop a para-consistent logic. These motivations are formally developed using semantic ideas, and we employ, in particular, bivaluations and truth-tables to characterise this logic. After discussing these ideas, we examine some applications of paraconsistent logic to various domains. With these motivations and applications in hand, the usefulness of paraconsistent logic becomes hard to deny.


Classical Logic Trivial Theory Paraconsistent Logic Inconsistent Theory Inconsistent Belief 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arruda A.I. (1980). “A Survey of Paraconsistent Logic”, in Arruda, Chuaqui, and da Costa (eds.), pp. 1–41.Google Scholar
  2. Arruda A.I. (1989). “Aspects of the Historical Development of Paraconsistent Logic”, in Priest, Routley and Norman (eds.), pp. 99–130.Google Scholar
  3. Arruda A., Chuaqui R., and da Costa N.C.A. (eds.) (1980). Mathematical Logic in Latin America. Amsterdam: North-Holland.Google Scholar
  4. Béziau J.-Y. (1990). “Logiques construites suivant les méthodes de da Costa”, Logique et Analyse 131-132, pp. 259–272.Google Scholar
  5. Bishop E. (1967). Foundations of Constructive Analysis. New York: McGraw-Hill.Google Scholar
  6. da Costa N.C.A. (1963). “Calculs propositionnels pour les systèmes formels inconsistants”, Comptes-rendus de l’Académie des Sciences de Paris 257, pp. 3790–3793.Google Scholar
  7. ____ (1986). “On Paraconsistent Set Theory”, Logique et Analyse 115, pp. 361–371.Google Scholar
  8. da Costa N.C.A. (1989). “Mathematics and Paraconsistency (in Portuguese)”, Monografias da Sociedade Paranaense de Matemática 7. Curitiba: UFPR.Google Scholar
  9. ____ (2000). “Paraconsistent Mathematics”, in D. Batens, C. Mortensen, G. Priest and J.-P. Van Bendegem (eds.), Frontiers of Paraconsistency. Dordrecht: Kluwer Academic Publishers.Google Scholar
  10. da Costa N.C.A. and Alves E.H. (1977). “A Semantic Analysis of the Calculi Cn”, Notre Dame Journal of Formal Logic 16, pp. 621–630.Google Scholar
  11. da Costa N.C.A. and Béziau, J.-Y. (1994). “Théorie de la valuation”, Logique et Analyse 146, pp. 95–117.Google Scholar
  12. da Costa, N.C.A. Béziau J.-Y. and Bueno O. (1995a). “Aspects of Paraconsistent Logic”, Bulletin of the Interest Group in Pure and Applied Logics 3, pp. 597–614.Google Scholar
  13. ____ (1995b). “Paraconsistent Logic in a Historical Perspective”, Logique et Analyse 150-151-152, pp. 111–125.Google Scholar
  14. ____ (1996). “Malinowski and Suszko on Many-Valuedness: On the Reduction of Many-Valuedness to Two-Valuedness,” Modern Logic 6, pp. 272–299.Google Scholar
  15. ____ (1998). Elements of Paraconsistent Set Theory (in Portuguese). Campinas: Coleção CLE.Google Scholar
  16. da Costa N.C.A. and Bueno O. (1996). “Consistency, Paraconsistency and Truth (Logic, the Whole Logic and Nothing but the Logic)”, Ideas y Valores 100, pp. 48–60.Google Scholar
  17. ____ (1997). “Review of Chris Mortensen (1995)”, Journal of Symbolic Logic 62, pp. 683–685.Google Scholar
  18. ____ (2001). “Paraconsistency: Towards a Tentative Interpretation”, Theoria 16, pp. 119–145.Google Scholar
  19. da Costa N.C.A., Bueno O. and Béziau J.-Y. (1995). “What is Semantics? A Brief Note on a Huge Question”, Sorites — Electronic Quarterly of Analytical Philosophy 3, pp. 43–47.Google Scholar
  20. da Costa N.C.A., Bueno O. and French S. (1998). “Is There a Zande Logic?”, History and Philosophy of Logic 19, pp. 41–54.Google Scholar
  21. da Costa N.C.A. and French S. (1988). “Belief and Contradiction”, Crítica XX, pp. 3–11.Google Scholar
  22. ____ (1989). “On the Logic of Belief”, Philosophy and Phenomenological Research XLIX, pp. 431–446.Google Scholar
  23. ____ (1990). “Belief, Contradiction and the Logic of Self-Deception”, American Philosophical Quarterly 27, pp. 179–197.Google Scholar
  24. ____ (1995). “Partial Structures and the Logic of the Azande”, American Philosophical Quarterly 32, pp. 325–339.Google Scholar
  25. da Costa N.C.A. and Subrahmanian V.S. (1989). “Paraconsistent Logics as a Formalism for Reasoning About Inconsistent Knowledge Bases”, Artificial Intelligence in Medicine 1, pp. 167–174.Google Scholar
  26. D’Ottaviano I. (1990). “On the Development of Paraconsistent Logic and da Costa’s Work”, Journal of Non-Classical Logic 7, pp. 89–152.MathSciNetGoogle Scholar
  27. Dummett M. (1977). Elements of Intuitionism. Oxford: Clarendon Press.Google Scholar
  28. French S. (1990). “Rationality, Consistency and Truth”, Journal of Non-Classical Logic 7, pp. 51–71.MathSciNetGoogle Scholar
  29. Heyting A. (1971). Intuitionism: An Introduction. (3rd edition.) Amsterdam: North-Holland.Google Scholar
  30. Mortensen C. (1995). Inconsistent Mathematics. Dordrecht: Kluwer Academic Publishers.Google Scholar
  31. Poincaré H. (1905). Science and Hypothesis. New York: Dover.Google Scholar
  32. Priest G., Routley R. and Norman J. (ed.) (1989). Paraconsistent Logic: Essays on the Inconsistent. Munich: Philosophia.Google Scholar
  33. Suszko R. (1975). “Remarks on Lukasiewicz’s Three-Valued Logic”, Bulletin of the Section of Logic 4, pp. 87–90.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Newton C.A. da Costa
    • 1
  • Jean-Yves Béziau
    • 2
  • Otávio Bueno
    • 3
  1. 1.University of São PauloSão Paulo
  2. 2.Institut de LogiqueUniversité de NeuchâtelNeuchâtel
  3. 3.University of South CarolinaUSA

Personalised recommendations