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Geometric Interpretation of Strong Inconsistency in Knowledge Based Systems

In: Computer Algebra in Scientific Computing CASC’99

Author

Listed:
  • E. Roanes-Lozano

    (Universidad Complutense de Madrid, Dept. Algebra, Edificio “Almudena”)

  • E. Roanes-Macías

    (Universidad Complutense de Madrid, Dept. Algebra, Edificio “Almudena”)

  • L. M. Laita

    (Universidad Politécnica de Madrid, Dept. Artificial Intelligence, Campus de Montegancedo)

Abstract

This paper distinguishes between two different kinds of inconsistency of rule-based Knowledge Based Systems (KBSs) constructed on multi-valued logics, which we have denoted “weak inconsistency” and “strong inconsistency”, respectively. While “weak inconsistency” is the inconsistency studied in the verification related references listed at the end of the article, “strong inconsistency” is introduced in this paper. “Strong inconsistency” is a particular case of “weak inconsistency”. An interesting interpretation in terms of polynomial ideals and (discrete) algebraic varieties is provided. Finally, an implementation in the Computer Algebra System (CAS) Maple is included. This implementation provides both a visualization of “strong inconsistency” and symbolic results (directly handling truth tables).

Suggested Citation

  • E. Roanes-Lozano & E. Roanes-Macías & L. M. Laita, 1999. "Geometric Interpretation of Strong Inconsistency in Knowledge Based Systems," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC’99, pages 349-363, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-60218-4_29
    DOI: 10.1007/978-3-642-60218-4_29
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