It is known that the OWL 2 RL Web Ontology Language Profile has PTime data complexity and can be translated into Datalog. However, the result of translation may consist of a Datalog program and a set of constraints in the form of negative clauses. Therefore, a knowledge base in OWL 2 RL may be unsatisfiable. In the current paper we first identify a maximal fragment of OWL 2 RL, called OWL 2 RL + , with the property that every knowledge base expressed in OWL 2 RL + can be translated to a Datalog

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... program and hence is satisfiable. We then propose some extensions of OWL 2 RL and OWL 2 RL + that still have PTime data complexity. Example 3.1. All the following knowledge bases in OWL 2 RL 0 are unsatisfiable: KB 1 = {A ≡ ⊥, A(a)}, KB 2 = {A ⊥, A(a)}, KB 3 = {A ¬B, A(a), B(a)}, KB 4 = {A ≤ 0 r.B, A(a), r(a, b), B(b)}, KB 5 = {A ≤ 0 r. , A(a), r(a, b)}, KB 6 = {A ≤ 0 σ.DT, A(a), σ(a, d), DT(d)}, KB 7 = {A ≤ 1 σ.DT, A(a), σ(a, d 1 ), DT(d 1 ), σ(a, d 2 ), DT(d 2 )}, where d 1 = d 2 , KB 8 = {Disj(A, B), A(a), B(a)}, KB 9 = {Disj(r, s), r(a, b), s(a, b)}, KB 10 = {Disj(σ, σ ), σ(a, d), σ (a, d)}, KB 11 = {Irref(r), r(a, a)}, KB 12 = {Irref(r), s r, r • r r, s(a, b), r(b, a)},