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An Invitation to New Essays on Belnap-Dunn Logic

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New Essays on Belnap-­Dunn Logic

Part of the book series: Synthese Library ((SYLI,volume 418))

Abstract

In this introductory note, we place the new essays on Belnap-Dunn logic, FDE, of the present volume against the background of the development of FDE. This note is an invitation to study the volume. It presents a chronological perspective on Belnap-Dunn logic and a slightly idiosyncratic list of further research topics.

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References

  1. Ahmad Almukdad and David Nelson. Constructible falsity and inexact predicates. The Journal of Symbolic Logic, 49(1):231–233, 1984.

    Article  Google Scholar 

  2. Alan Anderson and Nuel Belnap. Tautological entailments. Philosophical Studies, 13:9– 24, 1962.

    Google Scholar 

  3. Ofer Arieli and Arnon Avron. Reasoning with logical bilattices. Journal of Logic, Language and Information, 5:25–63, 1996.

    Article  Google Scholar 

  4. Nuel Belnap. How a computer should think. In G. Ryle, editor, Contemporary aspects of philosophy, pages 30–55. Oriel Press, 1977.

    Google Scholar 

  5. Nuel Belnap. A useful four-valued logic. In J.M. Dunn and G. Epstein, editors, Modern Uses of Multiple-Valued Logic, pages 8–37. D. Reidel Publishing Co., 1977.

    Google Scholar 

  6. Francesco Berto. A modality called ‘negation’. Mind, 124(495):761–793, 2015.

    Article  Google Scholar 

  7. Francesco Berto and Greg Restall. Negation on the Australian plan. Journal of Philosophical Logic, 2019. https://doi.org/10.1007/s10992-019-09510-2.

  8. Michael De and Hitoshi Omori. There is more to negation than modality. Journal of Philosophical logic, 47(2):281–299, 2018.

    Article  Google Scholar 

  9. Didier Dubois. On ignorance and contradiction considered as truth-values. Logic Journal of the IGPL, 16(2):195–216, 2008.

    Article  Google Scholar 

  10. J. Michael Dunn. Intuitive semantics for first-degree entailment and ‘coupled trees’. Philosophical Studies, 29:149–168, 1976.

    Article  Google Scholar 

  11. Melvin Fitting. Bilattices are nice things. In V. Hendricks and S.A. Pedersen, editors, Self-Reference, pages 53–77. CSLI-Publications, Stanford, 2004.

    Google Scholar 

  12. Matthew L. Ginsberg. Multivalued logics: A uniform approach to reasoning in AI. Computer Intelligence, 4:256–316, 1988.

    Google Scholar 

  13. Laurence R. Horn and Heinrich Wansing. Negation. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/negation/, Spring 2015 edition, 2015.

  14. Lloyd Humberstone. Negation by iteration. Theoria, 61(1):1–24, 1995.

    Article  Google Scholar 

  15. Lloyd Humberstone. Contra-classical logics. Australasian Journal of Philosophy, 78(4):438–474, 2000.

    Article  Google Scholar 

  16. Norihiro Kamide and Heinrich Wansing. Proof theory of Nelson’s paraconsistent logic: A uniform perspective. Theoretical Computer Science, 415:1–38, 2012.

    Article  Google Scholar 

  17. Norihiro Kamide and Heinrich Wansing. Proof Theory of N4-related Paraconsistent Logics. Studies in Logic, Vol. 54. College Publications, London, 2015.

    Google Scholar 

  18. Andreas Kapsner. Logics and Falsifications, volume 40 of Trends in Logic. Springer, 2014.

    Google Scholar 

  19. Hector J Levesque. A logic of implicit and explicit belief. In Proceedings of AAAI 1984, pages 198–202, 1984.

    Google Scholar 

  20. João Marcos. The value of the two values. In J.-Y. Béziau and M.E. Coniglio, editors, Logic without Frontiers: Festschrift for Walter Alexandre Carnielli on the occasion of his 60th birthday, pages 277–294. College Publication, 2011.

    Google Scholar 

  21. David Nelson. Constructible falsity. The Journal of Symbolic Logic, 14(1):16–26, 1949.

    Article  Google Scholar 

  22. Sergei P. Odintsov. Constructive Negations and Paraconsistency. Dordrecht: SpringerVerlag, 2008.

    Book  Google Scholar 

  23. Sergei P. Odintsov and Heinrich Wansing. Modal logics with belnapian truth values. Journal of Applied Non-Classical Logics, 20:279–301, 2010.

    Article  Google Scholar 

  24. Sergei P Odintsov and Heinrich Wansing. Disentangling FDE-based paraconsistent modal logics. Studia Logica, 105(6):1221–1254, 2017.

    Google Scholar 

  25. Hitoshi Omori and Heinrich Wansing. 40 years of FDE: an introductory overview. Studia Logica, 105(6):1021–1049, 2017.

    Article  Google Scholar 

  26. Hitoshi Omori and Heinrich Wansing. On Contra-classical variants of Nelson logic N4 and its classical extension. Review of Symbolic Logic, 11(4):805–820, 2018.

    Article  Google Scholar 

  27. Hitoshi Omori and Heinrich Wansing. Connexive logics. an overview and current trends. Logic and Logical Philosophy, pages 1–17, 2019.

    Google Scholar 

  28. Andreas Pietz and Umberto Rivieccio. Nothing but the truth. Journal of Philosophical Logic, 42:125–135, 2013.

    Article  Google Scholar 

  29. Graham Priest. The Logic of the Catuskoti. Comparative Philosophy, 1(2):24–54, 2010.

    Google Scholar 

  30. Graham Priest. Plurivalent Logics. The Australasian Journal of Logic, 11(1):1–13, 2014.

    Article  Google Scholar 

  31. Richard Routley. The American plan completed: Alternative classical-style semantics, without stars, for relevant and paraconsistent logics. Studia Logica, 43(1-2):131–158, 1984.

    Article  Google Scholar 

  32. Yaroslav Shramko. Dual-Belnap logic and anything but falsehood. IfCoLog Journal of Logics and their Applications, 6(2):411–430, 2019.

    Google Scholar 

  33. Yaroslav Shramko, J. Michael Dunn, and Tatsutoshi Takenaka. The trilattice of constructive truth values. Journal of Logic and Computation, 11(6):761–788, 2001.

    Google Scholar 

  34. Yaroslav Shramko and Heinrich Wansing. Some useful 16-valued logics: How a computer network should think. Journal of Philosophical Logic, 34(2):121–153, 2005.

    Article  Google Scholar 

  35. Yaroslav Shramko and Heinrich Wansing. Truth and Falsehood. An Inquiry into Generalized Logical Values. Trends in Logic. Vol. 36. Springer, Berlin, 2011.

    Google Scholar 

  36. Yaroslav Shramko, Dmitry Zaitsev, and Alexander Belikov. First-degree entailment and its relatives. Studia Logica, 105(6):1291–1317, 2017.

    Article  Google Scholar 

  37. Damian Szmuc and Hitoshi Omori. A Note on Goddard and Routley’s Significance Logic. The Australasian Journal of Logic, 15(2):431–448, 2018.

    Article  Google Scholar 

  38. Heinrich Wansing. The Logic of Information Structures. Springer Lecture Notes in AI 681. Springer, Berlin, 1993.

    Google Scholar 

  39. Heinrich Wansing. Connexive logic. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/fall2014/entries/logicconnexive/, Fall 2014 edition, 2014.

  40. Heinrich Wansing and Nuel Belnap. Generalized truth values. A reply to Dubois. Logic Journal of IGPL, 18(6):921–935, 2009.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Philosophy I, Ruhr-Universität, Bochum, Germany

    Hitoshi Omori & Heinrich Wansing

Authors
  1. Hitoshi Omori
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  2. Heinrich Wansing
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Correspondence to Hitoshi Omori .

Editor information

Editors and Affiliations

  1. Ruhr-University Bochum, Bochum, Germany

    Hitoshi Omori

  2. Ruhr-University Bochum, Bochum, Germany

    Heinrich Wansing

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Omori, H., Wansing, H. (2019). An Invitation to New Essays on Belnap-Dunn Logic . In: Omori, H., Wansing, H. (eds) New Essays on Belnap-­Dunn Logic. Synthese Library, vol 418. Springer, Cham. https://doi.org/10.1007/978-3-030-31136-0_1

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