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A paraconsistent semantics with contradiction support detection

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Logic Programming And Nonmonotonic Reasoning (LPNMR 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1265))

Abstract

We begin by motivating the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples. Next we overview WFSX P and present its embedding into WFS. We then address the problem of detecting contradiction support and relate it to WFSX p's intrinsic properties. Afterwards, we show how to implement two recent modal contradiction related constructs in the language of extended logic programs in order to gain explicit control of contradiction propagation. We finish by making comparisons and drawing some conclusions.

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References

  1. J. J. Alferes, C. V. Damásio, and L. M. Pereira. A logic programming system for non-monotonic reasoning. Journal of Automated Reasoning, 14(1):93–147, 1995.

    Google Scholar 

  2. J. J. Alferes and L. M. Pereira. Reasoning with Logic Programming, volume LNAI vol. 1111. Springer-Verlag, 1996. In print.

    Google Scholar 

  3. J. J. Alferes, L. M. Pereira, and T. Przymusinski. Strong and explicit negation in non-monotonic reasoning and logic programs. In JELIA '96, European Workshop on Logic in Artificial Intelligence. Springer-Verlag, 1996.

    Google Scholar 

  4. A. Almukdad and D. Nelson. Constructible falsity and inexact predicates. JSL, 49:231–233, 1984.

    Google Scholar 

  5. C. Baral and M. Gelfond. Logic programming and knowledge representation. Journal of Logic Programming, 19/20:73–148, 1994.

    Google Scholar 

  6. N. D. Belnap. A useful four-valued logic. In G. Epstein and J. M. Dunn, editors, Modern Uses of Many-valued Logic, pages 8–37. Reidel, 1977.

    Google Scholar 

  7. H. A. Blair and V. S. Subrahmanian. Paraconsistent logic programming. Theoretical Computer Science, 68:135–154, 1989.

    Google Scholar 

  8. N. Costa. On the theory of inconsistency formal system. Notre Dame Journal of Formal Logic, 15:497–510, 1974.

    Google Scholar 

  9. C. V. Damásio. Paraconsistent Extended Logic Programming with Constraints. PhD thesis, Universidade Nova de Lisboa, October 1996. 350 páginas.

    Google Scholar 

  10. J. Dix. A Classification-Theory of Semantics of Normal Logic Programs: I. Strong Properties. Fundamenta Informaticae, XXII(3):227–255, 1995.

    Google Scholar 

  11. J. Dix. A Classification-Theory of Semantics of Normal Logic Programs: II. Weak Properties. Fundamenta Informaticae, XXII(3):257–288, 1995.

    Google Scholar 

  12. W. Drabent and M. Martelli. Strict completion of logic programs. New Generation Computing, 9(1):69–79, 1991.

    Google Scholar 

  13. M. Fitting. Bilattices and the semantics of logic programming. Journal of Logic Programming, 11:91–116, 1991.

    Google Scholar 

  14. M. Fitting. Well-founded semantics, generalized. Journal of Logic Programming, 12:71–84, 1992.

    Google Scholar 

  15. J. Fox, P. Krause, and S. Ambler. Arguments, contradictions and practical reasoning. In B. Neumann, editor, ECAI'92, pages 623–627. John Wiley & Sons, 1992.

    Google Scholar 

  16. M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In R. Kowalski and K. A. Bowen, editors, ICLP'88, pages 1070–1080. MIT Press, 1988.

    Google Scholar 

  17. M. Gelfond and V. Lifschitz. Logic programs with classical negation. In Warren and Szeredi, editors, ICLP'90, pages 579–597. MIT Press, 1990.

    Google Scholar 

  18. R. Kowalski and F. Sadri. Logic programs with exceptions. In Warren and Szeredi, editors, 7th International Conference on Logic Programming. MIT Press, 1990.

    Google Scholar 

  19. J. Lin. A semantics for reasoning consistently in the presence of inconsistency. Artificial Intelligence, 86:75–95, 1996.

    Google Scholar 

  20. D. Nelson. Constructible falsity. Journal of Symbolic Logic, 14:16–26, 1949.

    Google Scholar 

  21. D. Pearce. Reasoning with Negative Information, II: hard negation, strong negation and logic programs. In D. Pearce and H. Wansing, editors, Nonclassical logic and information processing, LNAI 619, pages 63–79. Springer-Verlag, 1992.

    Google Scholar 

  22. D. Pearce. Answer sets and constructive logic, II: Extended logic programs and related non-monotonic formalisms. In L. Pereira and A. Nerode, editors, LPNMR'93, pages 457–475. MIT Press, 1993.

    Google Scholar 

  23. D. Pearce and G. Wagner. Reasoning with negative information I: Strong negation in logic programs. In L. Haaparanta, M. Kusch, and I. Niiniluoto, editors, Language, Knowledge and Intentionality, pages 430–453. Acta Philosophica Fennica 49, 1990.

    Google Scholar 

  24. D. Pearce and G. Wagner. Logic programming with strong negation. In P. Schroeder-Heister, editor, ELP'91, pages 311–326. LNAI 475, Springer-Verlag, 1991.

    Google Scholar 

  25. L. M. Pereira and J. J. Alferes. Well founded semantics for logic programs with explicit negation. In B. Neumann, editor, European Conference on Artificial Intelligence, pages 102–106, Wien, Austria, August 1992. John Wiley & Sons.

    Google Scholar 

  26. L. M. Pereira, J. J. Alferes, and J. N. Aparício. Contradiction Removal within Well Founded Semantics. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, Logic Programming and Nonmonotonic Reasoning, pages 105–119, Washington, USA, June 1991. MIT Press.

    Google Scholar 

  27. L. M. Pereira, C. V. Damásio, and J. J. Alferes. Debugging by diagnosing assumptions. In P. A. Fritzson, editor, Automatic Algorithmic Debugging, AADEBUG'93, LNCS 749, pages 58–74. Springer-Verlag, 1993.

    Google Scholar 

  28. L. M. Pereira, C. V. Damásio, and J. J. Alferes. Diagnosis and debugging as contradiction removal. In L. M. Pereira and A. Nerode, editors, 2nd Int. Workshop on Logic Programming and Non-Monotonic Reasoning, pages 334–348. The MIT Press, 1993.

    Google Scholar 

  29. L. M. Pereira, C. V. Damásio, and J. J. Alferes. Diagnosis and debugging as contradiction removal in logic programs. In L. Damas and M. Filgueiras, editors, Progress in Artificial Intelligence. Proceedings of the 6th Portuguese AI Conf., LNAI 727, pages 183–197. Springer-Verlag, 1993.

    Google Scholar 

  30. S. G. Pimentel and W. L. Rodi. Belief revision and paraconsistency in a logic programming framework. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LPNMR'91, pages 228–242. MIT Press, 1991.

    Google Scholar 

  31. G. Priest, R. Routley, and J. Norman. Paraconsistent logics. Philosophia Verlag, 1988.

    Google Scholar 

  32. T. Przymusinski. Extended stable semantics for normal and disjunctive programs. In Warren and Szeredi, editors, ICLP'90, pages 459–477. MIT Press, 1990.

    Google Scholar 

  33. N. Rescher and R. Brandom. The logic of inconsistency. Basil Blackwell, 1980.

    Google Scholar 

  34. C. Sakama. Extended well-founded semantics for paraconsistent logic programs. In Fifth Generation Computer Systems, pages 592–599. ICOT, 1992.

    Google Scholar 

  35. C. Sakama and K. Inoue. Paraconsistent Stable Semantics for extended disjunctive programs. Journal of Logic and Computation, 5(3):265–285, 1995.

    Google Scholar 

  36. G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357–371. LNCS 495, Springer-Verlag, 1991.

    Google Scholar 

  37. G. Wagner. Reasoning with inconsistency in extended deductive databases. In L. M. Pereira and A. Nerode, editors, LPNMR'93, pages 300–315. MIT Press, 1993.

    Google Scholar 

  38. G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. Lecture Notes on Artificial Intelligence, 764, 1994.

    Google Scholar 

  39. M. Wallace. Tight, consistent, and computable completions for unrestricted logic programs. Journal of Logic Programming, 15:243–273, 1993.

    Google Scholar 

  40. J.-H. You, S. Ghosh, L.-Y. Yuan, and R. Goebel. An introspective framework for paraconsistent logic programs. In J. W. Lloyd, editor, ILPS95. The MIT Press, 1995.

    Google Scholar 

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Authors and Affiliations

  1. Rua da Escola Politécnica 141-147, Universidade Aberta, 1250, Lisboa, Portugal

    Carlos Viegas Damásio

  2. CITIA, Departamento de Informática, U. Nova de Lisboa, 2825, Monte da Caparica, Portugal

    Carlos Viegas Damásio & Luís Moniz Pereira

Authors
  1. Carlos Viegas Damásio
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  2. Luís Moniz Pereira
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Jürgen Dix Ulrich Furbach Anil Nerode

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© 1997 Springer-Verlag Berlin Heidelberg

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Damásio, C.V., Pereira, L.M. (1997). A paraconsistent semantics with contradiction support detection. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_18

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  • DOI: https://doi.org/10.1007/3-540-63255-7_18

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  • Print ISBN: 978-3-540-63255-9

  • Online ISBN: 978-3-540-69249-2

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