Skip to main content
SpringerLink
Log in
Book cover

European Workshop on Logics in Artificial Intelligence

JELIA 1996: Logics in Artificial Intelligence pp 404–416Cite as

A simple signed system for paraconsistent reasoning

  • Belief Revision and Paraconsistency
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1126))

Abstract

We present a novel approach to paraconsistent reasoning, that is to reasoning from inconsistent information. The basic idea is the following. We transform an inconsistent theory into a consistent one by renaming all literals occuring in the theory. Then, we restore some of the original contents of the theory by introducing progressively formal equivalences linking the original literals to their renamings. This is done as long as consistency is preserved. The restoration of the original contents of the theory is done by appeal to default logic. The overall approach provides us with a family of paraconsistent consequence relations.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Anderson and N. Belnap. Entailment: The Logic of Relevance and Necessity, Vol. I. Princeton University Press, 1975.

    Google Scholar 

  2. O. Arieli and A. Avron. Logical bilattices and inconsistent data. In Proceedings of the Logic in Computer Science Conference, pages 468–476, 1994.

    Google Scholar 

  3. N. Belnap. A useful four-valued logic. In J. Dunn and G. Epstein, editors, Modern Uses of Multiple-Valued Logic. Reidel, 1977.

    Google Scholar 

  4. S. Benferhat, D. Dubois, and H. Prade. Argumentative inference in uncertain and inconsistent knowledge bases. In Proceedings of Ninth International Conference on Uncertainty in Artificial Intelligence, pages 411–419, 1993.

    Google Scholar 

  5. P. Besnard. Paraconsistent logic approach to knowledge representation. In M. de Glas and D. Gabbay, editors, Proceedings of the First World Conference on Fundamentals of Artificial Intelligence, 1991.

    Google Scholar 

  6. P. Besnard and T. Schaub. A simple signed system for paraconsistent reasoning. Technical report, IRISA, 1996. In preparation.

    Google Scholar 

  7. S. Brass. On the semantics of supernormal defaults. In Ruzena Bajcsy, editor, Proceedings of the International Joint Conference on Artificial Intelligence, pages 578–583. Morgan Kaufmann Publishers, 1993.

    Google Scholar 

  8. G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

    Google Scholar 

  9. W. Carnielli, L. Fariñas del Cerro, and M. Lima Marques. Contextual negations and reasoning with contradictions. In J. Mylopoulos and R. Reiter, editors, Proceedings of the International Joint Conference on Artificial Intelligence, pages 532–537. Morgan Kaufmann Publishers, 1991.

    Google Scholar 

  10. N. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15:497–510, 1974.

    Google Scholar 

  11. J. Dix. On cumulativity in default logic and its relation to Poole's approach. In B. Neumann, editor, Proceedings of the European Conference on Artificial Intelligence, pages 289–293. John Wiley & sons, 1992.

    Google Scholar 

  12. D. Gabbay and A. Hunter. Restricted access logics for inconsistent information. In M. Clarke, R. Kruse, and S. Moral, editors, Proceedings of European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty. Springer Verlag, 1993.

    Google Scholar 

  13. J. Horty, R. Thomason, and D. Touretzky. A skeptical theory of inheritance in nonmonotonic semantic networks. Artificial Intelligence, 42:311–348, 1990.

    MathSciNet  Google Scholar 

  14. M. Kifer and E. Lozinskii. RI: A logic for reasoning with inconsistency. In Proceedings of the Logic in Computer Science Conference, pages 253–262, 1989.

    Google Scholar 

  15. D. Makinson. General theory of cumulative inference. In M. Reinfrank, J. de Kleer, M. Ginsberg, and E. Sandewall, editors, Proceedings of the Second International Workshop on Non-Monotonic Reasoning, volume 346 of Lecture Notes in Artificial Intelligence, pages 1–18. Springer Verlag, 1989.

    Google Scholar 

  16. R. Manor and N. Rescher. On inferences from inconsistent information. Theory and Decision, 1:179–219, 1970.

    Article  Google Scholar 

  17. T. Pequeno and A. Buchsbaum. The logic of epistemic inconsistency. In J. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning, pages 453–560, San Mateo, CA, 1991. Morgan Kaufmann Publishers.

    Google Scholar 

  18. D. Poole. A logical framework for default reasoning. Artificial Intelligence, 36:27–47, 1988.

    MathSciNet  Google Scholar 

  19. G. Priest, R. Routley, and J. Norman, editors. Paraconsistent Logics. Philosophica Verlag, 1989.

    Google Scholar 

  20. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1–2):81–132, 1980.

    Article  Google Scholar 

  21. R. Reiter. A theory of diagnosis from first principles. Artificial Intelligence, 32(1):57–96, 1987.

    Article  Google Scholar 

  22. N. Rescher and R. Brandom. The Logic of Inconsistency. Blackwell, 1980.

    Google Scholar 

  23. N. Roos. A logic for reasoning with inconsistent knowledge. Artificial Intelligence, 57:69–103, 1992.

    Article  Google Scholar 

  24. E. Sandewall. A functional approach to non-monotonic logic. Computational Intelligence, 1:80–87, 1985.

    Google Scholar 

  25. G. Wagner. Ex contradictione nihil sequitur. In J. Mylopoulos and R. Reiter, editors, Proceedings of the International Joint Conference on Artificial Intelligence, pages 538–543. Morgan Kaufmann Publishers, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRISA, Campus de Beaulieu, F-35042, Rennes Cedex

    Philippe Besnard

  2. Faculté de Sciences, Université d'Angers, 2 Boulevard Lavoisier, F-49045, Angers Cedex 01

    Torsten Schaub

Authors
  1. Philippe Besnard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Torsten Schaub
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

José Jülio Alferes Luís Moniz Pereira Ewa Orlowska

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Besnard, P., Schaub, T. (1996). A simple signed system for paraconsistent reasoning. In: Alferes, J.J., Pereira, L.M., Orlowska, E. (eds) Logics in Artificial Intelligence. JELIA 1996. Lecture Notes in Computer Science, vol 1126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61630-6_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-61630-6_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61630-6

  • Online ISBN: 978-3-540-70643-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation