Foundations of Semantic Web Technologies

Ontologies and Rules 233

treme example, consider the simple fact → R(a, b) which could directly be

expressed as a SROIQ ABox statement. Instead, the algorithm normalizes

the rule to {a}(x)∧{b}(y) → R(x, y), and then connects both terms to obtain

{a}(x) ∧ U(x, y) ∧ {b}(y) → R(x, y). Finally, in Step 6b, unary atoms are

replaced by auxiliary binary predicates R

{a}

and R

{b}

, so that we obtain the

following final set of description logic axioms:

{a} ≡ ∃R

{a}

.Self

{b} ≡ ∃R

{b}

.Self

R

{a}

◦ U ◦ R

{b}

v R

While this is clearly not the preferred way of expressing this statement, it

still captures the intended semantics. On the other hand, the algorithm also

covers cases ...