A bottom-up method for the deterministic horn fragment of the description logic ALC

• Authors: Linh Anh Nguyen
• Venue: JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
• Year: 2006

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, P⊧C 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 2O(n) and returns a pseudo-interpretation of size 2O(n). Our method is extendable for instance checking w.r.t. knowledge bases containing also an ABox in more expressive description logics.