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

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.