Foundations of Semantic Web Technologies

390 Foundations of Semantic Web Technologies

Intelligent(x) ∨ Old(x) → IntelligentOrOld(x)

(IntelligentOrOld(x)) ∧ ∃y.(marriedWith(x, y)) → (Wise(x) ∧ Bald(x))

∨ ¬Male(x)

This will not reduce the number of datalog rules in this example (since 2×2

happens to be the same as 2 + 2), but it is generally sufficient to ensure that

Lloyd-Topor transformations lead to only a linear increase in the size of a rule

set. In other words, they are harmless for the performance of reasoning.

Solution to Exercise 6.2

1. C u ∃r.D v E

2. ∃r.Self v ∀s.>

3. ∃t.Self ≡ C ∧ ∃r

−

.E

∃d.Self ≡ D

t ◦ U ◦ d v s

Solution to Exercise 6.3

All the rules can be translated into SROIQ, as follows.

Intelligent v Clever

∃.knows.Intelligent v Clever

Sailor u ∃loves.Spinach u ∃loves.{olive_oyl} v