Abstract

Abstract. We study the deterministic Horn fragment of ALC, which restricts the general Horn fragment of 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 I of P such that for every deterministic positive concept C, P | = C iff I validates C (and more strongly, iff I,τ | = C, whereτ is the distinguished object of I and the satisfaction means τ is an instance of C w.r.t. 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. 1

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