A logic of supporters

  • Céline Lafage
  • Jérôme Lang
  • Régis Sabbadin
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 516)


In this paper we study carefully the notion of supporter (close to arguments, or ATMS labels). We investigate the lattice-theoretic properties of the set of supporters. We define support measures, and their duals, occasion measures, which appear to have many similarities with necessity and possibility measures respectively (up to change of the valuation lattice). These similarities enable us to define a supporter logic as an instance of the family of lattice-based generalisations of possibilistic logic.


Support Measure Belief Function Occasion Measure Supporter Logic Possibilistic Logic 
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  1. [1]
    L. Amgoud, C. Cayrol and D. Le Berre. Comparing arguments using preference orderings for argument-based reasoning. Proceedings of CTAI’96, 400–403, 1996.Google Scholar
  2. [2]
    S. Benferhat, D. Dubois and H. Prade. Argumantative inference in inconsistent knowledge bases. Proceedings of UAI’93 411–419.Google Scholar
  3. [3]
    G. Birkhoff, Lattice Theory, American Mathematical Society, Colloquium publications, Volume 25, 1967.Google Scholar
  4. [4]
    P. Chatalic, C. Froidevaux. Lattice-based graded logic: a multimodal approach. Proceedings of UAI’92, 33–40.Google Scholar
  5. [5]
    A. Darwiche. Argument calculus and networks. Proceedings of UAI’93,420–427.Google Scholar
  6. [6]
    J. de Kleer. An assumption-based TMS. Artificial Intelligence 28,127–162,1986.CrossRefGoogle Scholar
  7. [7]
    J. De Kleer, B. C. Williams. Diagnosis multiple faults. Dans W. Hamscher, L. Console, J. De Kleer, éditeurs, Readings in model-based diagnosis, pages 102–103.(1992)Google Scholar
  8. [8]
    D. Dubois, F. Dupin de Saint-Cyr, Jérôme Lang and Henri Prade. Weighted logics of uncertainty. In preparation.Google Scholar
  9. [9]
    D. Dubois, J. Lang, H. Prade. Timed possibilistic logic. Fundamenta Informaticae, 211–234, 1991.Google Scholar
  10. [10]
    D. Dubois, J. Lang, H. Prade. Dealing with multi-source information in possibilistic logic. Proceedings of ECAL92, 38–42.Google Scholar
  11. [11]
    D. Dubois, J. Lang, H. Prade. Possibilistic logic. Handbook of Logic in Artificial Intelligence and Logic Programming (D.M. Gabbay, C.J. Hogger, J.A. Robinson, eds.), Vol. 3, 439–513, Oxford University Press.Google Scholar
  12. [12]
    J. Fox, P. Krause and M. Elvang-Georansson. Argumantation as a general framework for uncertain reasoning. Proceedings of UAI’93,428–434.Google Scholar
  13. [13]
    D. Gabbay. Labelled Deductive Systems, Oxford University Press, 1991.Google Scholar
  14. [14]
    J. Kohlas and P.-A. Monney. Probabilistic assumption-based reasoning. Proceedings of UAI’93,485–491.Google Scholar
  15. [15]
    J. Kohlas and P.-A. Monney. A Mathematical Theory of Hints. Lecture Notes in Economics and Mathematical Systems, Vol. 425, Springer-Verlag, 1995.Google Scholar
  16. [16]
    K. Laskey and P. Lehner. Assumptions, beliefs and probabilities. Artificial Intelligence 41 (1989/90), 65–77.Google Scholar
  17. [17]
    D. Le Berre and R. Sabbadin. Decision-theoretic diagnosis and repair: representational and computational issues. Proceedings of DX’97, 141–145, 1997.Google Scholar
  18. [18]
    G. Provan. An analysis of mATMS-based techniques for computing Dempster-Shafer belief functions. Proceedings of IJCAT89,1115–1120.Google Scholar
  19. [19]
    P. Smets. Probability of deductibility and belief functions. Proceedings of ECSQARU’93. Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Céline Lafage
    • 1
  • Jérôme Lang
    • 1
  • Régis Sabbadin
    • 1
  1. 1.IRIT - Université Paul SabatierToulouse CedexFrance

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