On Drawing Conclusions in Presence of Inconsistent Data

  • Sylvia Encheva
  • Sharil Tumin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4953)


Most automated tests assessing students understanding of a concept contain one question requiring application of that concept. To attain a higher level of certainty in the evaluation process we propose a test with three different questions requiring application of one concept. Such a test is intended to facilitate the self-assessment process and can be suggested to students after a concept has been introduced. Lattice theory and higher-order logic are further applied for presenting a structure that can serve as a building block of an intelligent tutoring system.


five-valued logic automated tests 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belnap, N.J.: A useful four.valued logic. In: Dunn, J.M., Epstain, G. (eds.) Modern uses of multiple-valued logic, pp. 8–37. D. Reidel Publishing Co., Dordrecht (1977)Google Scholar
  2. 2.
    Davey, B.A., Priestley, H.A.: Introduction to lattices and order. Cambridge University Press, Cambridge (2005)Google Scholar
  3. 3.
    Ferreira, U.: A Five-valued Logic and a System. Journal of Computer Science and Technology 4(3), 134–140 (2004)Google Scholar
  4. 4.
    Goodstein, R.L.: Boolean Algebra. Dover Publications (2007)Google Scholar
  5. 5.
    Gradel, E., Otto, M., Rosen, E.: Undecidability results on two-variable logics. Archive of Mathematical Logic 38, 313–354 (1999)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Guzmàn, E., Conejo, R.: A model for student knowledge diagnosis through adaptive testing. In: Lester, J.C., Vicari, R.M., Paraguaçu, F. (eds.) ITS 2004. LNCS, vol. 3220, pp. 12–21. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Huffman, D., Goldberg, F., Michlin, M.: Using computers to create constructivist environments: impact on pedagogy and achievement. Journal of Computers in mathematics and science teaching 22(2), 151–168 (2003)Google Scholar
  8. 8.
    Immerman, N., Rabinovich, A., Reps, T., Sagiv, M., Yorsh, G.: The boundery between decidability and undecidability of transitive closure logics. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Kleene, S.: Introduction to Metamathematics. D. Van Nostrand Co., Inc., New York (1952)zbMATHGoogle Scholar
  10. 10.
  11. 11.
    Park, C., Kim, M.: Development of a Level-Based Instruction Model in Web-Based Education. LNCS (LNAI), vol. 3190, pp. 215–221. Springer, Heidelberg (2003)Google Scholar
  12. 12.
    Santos, C.T., Osòrio, F.S.: Integrating intelligent agents, user models, and automatic content categorization in virtual environment. In: Lester, J.C., Vicari, R.M., Paraguaçu, F. (eds.) ITS 2004. LNCS, vol. 3220, pp. 128–139. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Whitesitt, J.E.: Boolean Algebra and Its Applications. Dover Publications (1995)Google Scholar
  14. 14.
    Wille, R.: Concept lattices and conceptual knowledge systems. Computers Math. Applic. 23(6-9), 493–515 (1992)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sylvia Encheva
    • 1
  • Sharil Tumin
    • 2
  1. 1.Stord/Haugesund University CollegeHaugesundNorway
  2. 2.IT-Dept.University of BergenBergenNorway

Personalised recommendations