Deductive Inference for the Interiors and Exteriors of Horn Theories

  • Kazuhisa Makino
  • Hirotaka Ono
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


In this paper, we investigate the deductive inference for the interiors and exteriors of Horn knowledge bases, where the interiors and exteriors were introduced by Makino and Ibaraki [11] to study stability properties of knowledge bases. We present a linear time algorithm for the deduction for the interiors and show that it is co-NP-complete for the deduction for the exteriors. Under model-based representation, we show that the deduction problem for interiors is NP-complete while the one for exteriors is co-NP-complete. As for Horn envelopes of the exteriors, we show that it is linearly solvable under model-based representation, while it is co-NP-complete under formula-based representation. We also discuss the polynomially solvable cases for all the intractable problems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Kazuhisa Makino
    • 1
  • Hirotaka Ono
    • 2
  1. 1.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan
  2. 2.Department of Computer Science and Communication EngineeringKyushu UniversityFukuokaJapan

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