Advertisement

A unifying logical framework for reason maintenance

  • Detlef Fehrer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)

Abstract

We present a way to semantically describe reason maintenance systems, based on Gabbay's labelled deductive system idea. Our approach works for justification based as well as for assumption based methods, thus giving a unifying semantics to both of them. Instead of restricting ourselves to only propositional Horn clauses, we'll admit arbitrary logics, e.g. full first order language. This enables us to characterize systems as a whole, including both the reason maintenance component and the problem solver, nevertheless maintaining a separation between the basic logic and the part that describes the label propagation.

Keywords

Propositional Logic Basic Logic Belief Revision Default Logic Stable Model Semantic 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [dK86]
    Johan de Kleer. An Assumption-Based TMS. Artificial Intelligence, 28(1), pp. 127–162, 1986.Google Scholar
  2. [DLP90]
    Didier Dubois, Jérôme Lang, and Henri Prade. A Possibilistic Assumption-Based Truth Maintenance System with Uncertain Justifications, and its Application to Belief Revision. In J. P. Martins and M. Reinfrank, editors, Truth Maintenance Systems, volume 515 of Lecture Notes in Artificial Intelligence, pp. 87–106. Springer-Verlag, August 1990.Google Scholar
  3. [Doy79]
    Jon Doyle. A Truth Maintenance System. Artificial Intelligence, 12, pp. 231–272, 1979.Google Scholar
  4. [Elk90]
    Charles Elkan. A Rational Reconstruction of Nonmonotonic Truth Maintenance Systems. Artificial Intelligence, 43(2), pp. 219–234, 1990.Google Scholar
  5. [FH89]
    Yasushi Fujiwara and Shinichi Honiden. Relating the TMS to Autoepistemic Logic. In IJCAI-89. Eleventh International Joint Conference on Artificial Intelligence, volume 2, pp. 1199–1205, 1989.Google Scholar
  6. [FH90]
    Yasuchi Fujiwara and Shinichi Honiden. On logical foundations of the ATMS. In J. P. Martins and M. Reinfrank, editors, Truth Maintenance Systems, volume 515 of Lecture Notes in Artificial Intelligence, pp. 125–135. Springer-Verlag, August 1990.Google Scholar
  7. [Gab91]
    Dov Gabbay. Labelled Deductive Systems, Part I. CIS Bericht 90-22, Centrum für Informations-und Sprachverarbeitung, February 1991.Google Scholar
  8. [GM90a]
    Laura Giordano and Alberto Martelli. Generalized Stable Models, Truth Maintenance and Conflict Resolution. In David H. D. Warren and Peter Szeredi, editors, Logic Programming. Proceedings of the Seventh International Conference, Logic Programming Series, pp. 427–441, Cambridge, Massachusetts / London, England, 1990. MIT Press.Google Scholar
  9. [GM90b]
    Laura Giordano and Alberto Martelli. Truth Maintenance Systems and Belief Revision. In J. P. Martins and M. Reinfrank, editors, Truth Maintenance Systems, volume 515 of Lecture Notes in Artificial Intelligence, pp. 71–86. Springer-Verlag, August 1990.Google Scholar
  10. [GO92]
    Dov M. Gabbay and Hans Jürgen Ohlbach. From a Hilbert Calculus to its Model Theoretic Semantics. In Kryshna Broda, editor, Proceedings of the 4th UK Conference on Logic Programming, Workshops in Computing, pp. 218–252. Springer Verlag, 1992.Google Scholar
  11. [Goo87]
    James. W. Goodwin. A Theory and System for Non-Monotonic Reasoning. Linköping studies in science and technology, dissertation no. 165, Department of Computer and Information Science, Linköping University, S-581 83 Linköping, 1987.Google Scholar
  12. [Ino90]
    Katsumi Inoue. An Abductive Procedure for the CMS/ATMS. In J. P. Martins and M. Reinfrank, editors, Truth Maintenance Systems, volume 515 of Lecture Notes in Artificial Intelligence, pp. 34–53. Springer-Verlag, August 1990.Google Scholar
  13. [JK90]
    Ulrich Junker and Kurt Konolige. Computing the Extensions of Autoepistemic and Default Logics with a Truth Maintenance System. In Proceedings of the 8th AAAI, volume 1, pages 278–283, 1990.Google Scholar
  14. [Jun89]
    Ulrich Junker. A Correct Non-Monotonic ATMS. In Proc. of the IJCAI, 1989.Google Scholar
  15. [McA78]
    D. McAllester. A three valued truth maintenance system. AI Memo 473, AI lab, MIT Cambridge, 1978.Google Scholar
  16. [McD91]
    Drew McDermott. A general framework for reason maintenance. Artificial Intelligence, 50(3), pp. 289–329, 1991.Google Scholar
  17. [Mor87]
    P.H. Morris. Curing anomalous extensions. In Proceedings of the AAAI-87, pp. 437–442, Seattle, WA, 1987.Google Scholar
  18. [Mor88]
    Paul H. Morris. The Anomalous Extension Problem in Default Reasoning. Artificial Intelligence, 35(2), pp. 383–399, 1988.Google Scholar
  19. [MS83]
    João P. Martins and Stuart C. Shapiro. Reasoning in Multiple Belief Spaces. In Proceedings of the IJCAI83, pp. 370–373, 1983.Google Scholar
  20. [MS88]
    João P. Martins and Stuart C. Shapiro. A Model for Belief Revision. Artificial Intelligence, 35, pp. 25–79, 1988.Google Scholar
  21. [RDB89]
    Michael Reinfrank, Oskar Dressler, and Gerd Brewka. On the Relation Between Truth Maintenance and Autoepistemic Logic. In IJCAI-89. Eleventh International Joint Conference on Artificial Intelligence, volume 2, pp. 1206–1212, 1989.Google Scholar
  22. [RdK87]
    Raymond Reiter and Johan de Kleer. Foundations of Assumption-Based Truth Maintenance Systems: Preliminary Report. In Proceedings of the AAAI87, pp. 183–188, Seattle, Washington, July 1987.Google Scholar
  23. [Rei80]
    Raymond Reiter. A Logic for Default Reasoning. Artificial Intelligence, 13(1), pp. 81–132, 1980.Google Scholar
  24. [Wit90]
    Cees Witteveen. A Skeptical Semantics for Truth Maintenance. In J. P. Martins and M. Reinfrank, editors, Truth Maintenance Systems, volume 515 of Lecture Notes in Artificial Intelligence, pp. 136–154. Springer-Verlag, August 1990.Google Scholar
  25. [XH91]
    Wang Xianchang and Chen Huowang. On Semantics of TMS. In IJCAI-91. 12th International Joint Conference on Artificial Intelligence, volume 1, pp. 306–309, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Detlef Fehrer
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations