 Solution

The complete numbered axioms in the rule fragment RL description logic are $\boxed{(1),(3),(4)}$. Their translations to Datalog with constraints areThe first rule is (1). For (3), its existential antecedent needs a two-edge $R$ path ending at an $A$ or $B$ element. Split that disjunction into two Datalog rules, and use a separate variable $w$ for an arbitrary immediate $R$-successor of $x$. The conclusion applies to every such successor, not merely the path witness $y$.

The last rule is a constraint: a ground instance with both premises true makes the knowledge base inconsistent. If an implementation permits only positive Datalog heads, replace $\perp$ by a fresh nullary predicate $Bad$ and separately check that it is never derived. Merely deriving $Bad$ without that check would not express disjointness.

Axiom (2) requires an existential witness in its head and is outside RL description logic. Axiom (5), considered as the whole equivalence, is outside for the same reason in the direction $C⊑\exists P.\top$. If definitions are split before selecting eligible general concept inclusions, its reverse direction is eligible and adds $\boxed{P(x,y)\to C(x)}$. Keep the difference between selecting the complete equivalence and retaining its rule-expressible half explicit. The permitted positions of existential and universal restrictions are specified in the ^[ref].