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semantic-webowldescription-logic

Cyclic or Acyclic TBox

Is the following TBox cyclic or acyclic? If it is a cyclic TBox, how could it be converted to an acyclic one?

A ⊑ ¬E
E ⊑ ¬A

Solution

  • A ⊑ ¬E
    E ⊑ ¬A

    This TBox doesn't really say anything except that the classes A and E are disjoint. The subclass relations could be read as implications:

    • If something is an A, then it is not an E.
    • If something is an E, then it is not an A.

    To express disjointness in description logics, you'd typically say that the intersection of disjoint classes is equivalent, or a subclass, of the bottom concept, ⊥, which by definition has no instances. &bot is also the complement of the top concept, ⊤, which contains everything. Thus you could say any of the following:

    A ⊓ E ⊑ ⊥

    A ⊓ E ≡ ⊥

    A ⊓ E ⊑ ¬⊤

    A ⊓ E ≡ ¬⊤