A closer inspection of the formulas we obtain from translating knowledge bases into first-order logic reveals, that only the presence of the top role ∇ and role complement prevents Π(Γ) from being guarded for arbitrary knowledge bases Γ.
Consider the expressions ∀∇.A and ∀¬P.A. The translation of these expression is (∀y) (T → A(y)) and (∀y) (¬P(x, y) → A(y)), respectively. ...
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