A Bottom-Up Method for the Deterministic Horn Fragment of the Description Logic \(\mathcal{ALC}\)

  • Linh Anh Nguyen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4160)


We study the deterministic Horn fragment of \(\mathcal{ALC}\), which restricts the general Horn fragment of \(\mathcal{ALC}\) only in that, the constructor ∀R.C is allowed in bodies of program clauses and queries only in the form ∀ ∃ R.C, which is defined as ∀ R.C ⊓ ∃ R.C. We present an algorithm that for a deterministic positive logic program P given as a TBox constructs a finite least pseudo-model \(\mathcal{I}\) of P such that for every deterministic positive concept C, PC iff \(\mathcal{I}\) validates C (and more strongly, iff \(\mathcal{I},\tau \models C\), where τ is the distinguished object of \(\mathcal{I}\) and the satisfaction means τ is an instance of C w.r.t. \(\mathcal{I}\)). Pseudo-interpretations are very similar to (traditional) interpretations, except that they have two interpretation functions for roles, one to deal with the constructor ∃ R.C and the other to deal with ∀R.C. They are ordered by comparing the sets of validated positive concepts. Our algorithm runs in time 2 O(n) and returns a pseudo-interpretation of size 2 O(n). Our method is extendable for instance checking w.r.t. knowledge bases containing also an ABox in more expressive description logics.


Logic Program Modal Logic Description Logic Kripke Model Horn Clause 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Linh Anh Nguyen
    • 1
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland

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