Viewing hypothesis theories as constrained graded theories

  • Philippe Chatalic
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 838)


Modeling expert tasks often leads to consider uncertain and/or incomplete knowledge. This generally requires reasoning about uncertain beliefs and sometimes making additional hypotheses. While numerical models are often used to model uncertainty, the estimation of precise and meaningful values for certainty degrees is sometimes problematic. Moreover, the use of a numerical scale implies that any two certainty degrees are comparable. This paper presents a qualitative approach, where uncertainty is represented by means of partially ordered symbolic grades. The framework is a multimodal logic in which each grade is expressed as a modal operator. An extension of this framework is proposed which makes it possible to state additional hypotheses in the spirit of Siegel and Schwind's hypothesis theory. We show that such hypotheses may be interpreted as constraints on the set of possible beliefs. We thus obtain a very natural integration of multimodal graded logic and hypothesis theory. The resulting framework allows for the simultaneous representation of uncertain and/or incomplete information. Some correspondence results between extensions of graded default logic and those of such new graded hypothesis theories are established.


Uncertain and Incomplete knowledge representation and semantics Partially ordered grades Modal Logic Hypothesis theories 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Be 89]
    Besnard P. (1989), An introduction to default logic, Springer Verlag, Heidelberg.Google Scholar
  2. [Bi 73]
    Birkhoff G. (1973), Lattice Theory, American Mathematical Society Colloquium Publications, vol. XXV.Google Scholar
  3. [CF 91]
    Chatalic P. and Froidevaux C. (1991), Graded logics: A framework for uncertain and defeasible knowledge, in Methodologies for Intelligent Systems, (Ras Z.W. & Zemankova M. eds.), Proc. of ISMIS-91, Lecture Notes in Artificial Intelligence, 542, 479–489.Google Scholar
  4. [CF 92]
    Chatalic P. and Froidevaux C. (1992), Lattice based Graded logics: A multimodal Approach, Proc. Uncertainty in AI, Stanford, CA, USA, 33–40.Google Scholar
  5. [CF 93]
    Chatalic P. and Froidevaux C. (1993), A multimodal Approach to Graded Logic, L.R.I. Tech Report n∘ 808, L.R.I. Tech. Report, Université Paris-Sud, Orsay, France.Google Scholar
  6. [CF 93b]
    Chatalic P. and Froidevaux C. (1993), Weak inconsistency in graded default logic and hypothesis theory, DRUMS II Tech. Report 3.1.1. BRA n∘ 6156Google Scholar
  7. [CFS 94]
    Chatalic P., Froidevaux C. and Schwind C. (1994), A logic with graded hypotheses (forthcoming)Google Scholar
  8. [Ch 80]
    Chellas B. (1980), Modal logic — an introduction, Cambridge University Press, New York.Google Scholar
  9. [DL 91]
    Dubois D., Lang J. and Prade H., (1991), Inconsistency in knowledge bases — to live or not live with it-, Fuzzy Logic for the management of Uncertainty (Zadeh L.A., Kacprzyk J. eds) J. Wiley.Google Scholar
  10. [DP 88]
    Dubois D. and Prade H. (with the collaboration of Farreny H., Martin-Clouaire R., Testemale C.) (1988), Possibility Theory: An approach to computerized processing of uncertainty. Plenum Press, New-York.Google Scholar
  11. [Fi 73]
    Fine T.L. (1973) Theories of Probability: An Examination of Foundations. Academic Press, New York.Google Scholar
  12. [FG 90]
    Froidevaux C. and Grossetête C. (1990), Graded default theories for uncertainty, Proc. of the 9th European Conference on Artificial Intelligence, Stockholm, 283–288.Google Scholar
  13. [Gä 75]
    Gärdenfors P. (1975) Qualitative probability as an intensional logic, J. Phil. Logic 4, 171–185.Google Scholar
  14. [HR 87]
    Halpern J. and Rabin M. (1987) A logic to reason about likelihood, Artificial Intelligence 32, 379–405.Google Scholar
  15. [Ng 92]
    Nguyen F. (1992) Towards the introduction of inconsistency in the extensions of graded default theory. Research Note, LRI, Orsay. France.Google Scholar
  16. [Ni 86]
    Nilsson N.J. (1986) Probabilistic logic, Artificial Intelligence 28, 71–87.Google Scholar
  17. [Pe 88]
    Pearl J. (1988) Probabilistic Reasoning in Intelligent Systems — Networks of plausible Inference. Morgan Kaufmann Pub., San Matheo, Cal, USA.Google Scholar
  18. [Pg 92]
    Pereira Gonzalez W. (1992) Une logique modale pour le raisonnement dans l'incertain. PhD thesis. University of Rennes I, France.Google Scholar
  19. [Re 80]
    Reiter R. (1980) A logic for default reasoning, Artificial Intelligence 13, 81–132.Google Scholar
  20. [Re 87]
    Reiter R. (1987), Nonmonotonic reasoning, Annual Reviews Computer Science 2, 147–186.Google Scholar
  21. [SS 91]
    Siegel P. and Schwind C. (1991) Hypothesis Theory for Nonmonotonic Reasoning, 2nd Int. Workshop on Non-monotonic and Inductive Logic, Reinhardsbrunn Castle.Google Scholar
  22. [SS 93]
    Siegel P. and Schwind C. (1993) Modal logic based theory for non-monotonic reasoning, Journal of Applied Non-Classical Logics, Vol 3–1, pp 73–92Google Scholar
  23. [Sh 76]
    Shafer G. (1976) A mathematical theory of evidence, Princeton University Press, NJ, USA.Google Scholar
  24. [Vh 92]
    Van der Hoek W. (1992) On the Semantics of Graded Modalities, Journal of Applied Non Classical Logics, Vol. II n∘1, pp. 81–123.Google Scholar
  25. [WL 91]
    Wong S.K., Lingras P. and Yao Y. (1991) Propagation of Preference relations in qualitative inference networks, Proc. IJCAI 91, Sydney, Australia, 1204–1209.Google Scholar
  26. [Za 78]
    Zadeh L.A. (1978) Fuzzy Sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Philippe Chatalic
    • 1
  1. 1.Laboratoire de Recherche en InformatiqueUniversité Paris-SudOrsay CedexFrance

Personalised recommendations