Faculty of Computer Science Institute of Theoretical Computer Science, Chair of Automata Theory
Description Logic
Winter Semester 2017/18Exercise Sheet 6 21st November 2017
Prof. Dr.-Ing. Franz Baader, Dr.-Ing. Stefan Borgwardt
Exercise 6.1 We consider the tableau algorithmconsistent(T,A)for acyclic TBoxes T, which is obtained from consistent(A) by adding the ≡1-rule and the ≡2-rule for unfolding T. Prove that consistent(T,A)is a decision procedure for consistency ofALC-knowledge bases with acyclic TBoxes.
Exercise 6.2 Use the tableau algorithmconsistent(T,A)for acyclic TBoxes to determine whether the subsumption
¬(∀r.A)u ∀r.CvT ∀r.E holds w.r.t. the acyclic TBox
T ={C≡(∃r.¬B)u ¬A, D≡ ∃r.B, E≡ ¬(∃r.A)u ∃r.D}.
1
