Document Open Access Logo

Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency

Authors Ofer Arieli, Arnon Avron

PDF

File

Thumbnail PDF
PDF
LIPIcs.FSCD.2016.7.pdf
  • Filesize: 0.55 MB
  • 15 pages

Document Identifiers

Subject Classification

Keywords
  • Paraconsistecy
  • Paracompleteness
  • 4-valued logics

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Paradefinite (`beyond the definite') logics are logics that can be
used for handling contradictory or partial information. As such,
paradefinite logics should be both paraconsistent and paracomplete. In
this paper we consider the simplest semantic framework for defining
paradefinite logics, consisting of four-valued matrices, and study the
better accepted logics that are induced by these matrices.

Cite As Get BibTex

Ofer Arieli and Arnon Avron. Minimal Paradefinite Logics for Reasoning with Incompleteness and Inconsistency. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSCD.2016.7

Author Details

Ofer Arieli
Arnon Avron

References

  1. O. Arieli. Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae. ACM Transactions on Computational Logic, 8(3), 2007. Google Scholar
  2. O. Arieli and A. Avron. The value of the four values. Artificial Intelligence, 102(1):97-141, 1998. Google Scholar
  3. O. Arieli, A. Avron, and A. Zamansky. Ideal paraconsistent logics. Studia Logica, 99(1-3):31-60, 2011. Google Scholar
  4. O. Arieli and M. Denecker. Reducing preferential paraconsistent reasoning to classical entailment. Logic and Computation, 13(4):557-580, 2003. Google Scholar
  5. A. Avron. Simple consequence relations. Information and Computation, 92(1):105-140, 1991. Google Scholar
  6. A. Avron. On the expressive power of three-valued and four-valued languages. Journal of Logic and Computation, 9(6):977-994, 1999. Google Scholar
  7. A. Avron, J. Ben-Naim, and B. Konikowska. Processing information from a set of sources. In Towards Mathematical Philosophy, Trends in Logic, volume 10, pages 165-186. Springer, 2009. Google Scholar
  8. A. Avron and B. Konikowska. Multi-valued calculi for logics based on non-determinism. Logic Journal of the IGPL, 13(4):365-387, 2005. Google Scholar
  9. N. Belnap. How a computer should think. In G. Ryle, editor, Contemporary Aspects of Philosophy, pages 30-56. Oriel Press, 1977. Google Scholar
  10. N. Belnap. A useful four-valued logic. In J. M. Dunn and G. Epstein, editors, Modern Uses of Multiple-Valued Logics, pages 7-37. Reidel Publishing Company, 1977. Google Scholar
  11. J. Y. Béziau. Bivalent semantics for De Morgan logic (The uselessness of four-valuedness). In W. A. Carnielli, M. E. Coniglio, and I. M. L. D'Ottaviano, editors, The many sides of logic, pages 391-402. College Publication, 2009. Google Scholar
  12. F. Bou and U. Rivieccio. The logic of distributive bilattices. Logic Journal of the IGPL, 19(1):183-216, 2010. Google Scholar
  13. N. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497-510, 1974. Google Scholar
  14. J. M. Dunn. The Algebra of Intensional Logics. PhD thesis, University of Pittsburgh, Ann Arbor (UMI), 1966. Google Scholar
  15. J. M. Dunn. Intuitive semantics for first-degree entailments and coupled trees. Philosophical Studies, 29:149-168, 1976. Google Scholar
  16. M. Fitting. Bilattices and the semantics of logic programming. Journal of Logic Programming, 11(2):91-116, 1991. Google Scholar
  17. M. Fitting. The family of stable models. Journal of Logic Programming, 17:197-225, 1993. Google Scholar
  18. G. Gentzen. Investigations into logical deduction, 1934. In German. An English translation appears in `The Collected Works of Gerhard Gentzen', edited by M. E. Szabo, North-Holland, 1969. Google Scholar
  19. S. Gottwald. A treatise on many-valued logics. In Studies in Logic and Computation, volume 9. Research Studies Press, Baldock, 2001. Google Scholar
  20. G. Malinowski. Many-Valued Logics. Clarendon Press, 1993. Google Scholar
  21. D. J. Shoesmith and T. J. Smiley. Deducibility and many-valuedness. Journal of Symbolic Logic, 36:610-622, 1971. Google Scholar
  22. D. J. Shoesmith and T. J. Smiley. Multiple Conclusion Logic. Cambridge University Press, 1978. Google Scholar
  23. G. Takeuti. Proof Theory. Elsevier, 1975. Google Scholar
  24. A.S. Troelstra and H. Schwichtenberg. Basic Proof Theory. Cambridge University Press, 2000. Google Scholar
  25. A. Urquhart. Many-valued logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume II, pages 249-295. Kluwer, 2001. Second edition. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact