Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2015/knowledge-representation-and-reasoning/2/a/ii/solution

Absorb (4) using the equivalence
Thus we can take
Here is a primitive inclusion, handled by adding whenever labels a node. For literal substitution-based TBox unfolding, introduce a fresh description logic concept and replace the primitive inclusion by
This preserves the original models after forgetting : any model of the primitive inclusion extends by taking , and any model of the new definition satisfies the primitive inclusion. The fresh name is important. Replacing by alone would incorrectly assert that every non- element is an element.

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