Description Logic

Faculty of Computer Science Institute of Theoretical Computer Science, Chair of Automata Theory

Description Logic

Exercise Sheet 9 13th December 2017

Prof. Dr.-Ing. Franz Baader, Dr.-Ing. Stefan Borgwardt

Exercise 9.1 Determine whether Player1has a winning strategy in the following finite Boolean games, where in both casesΓ1={p₁,p₃}andΓ2={p₂,p₄}:

(a) ((p₁∧p₃)→ ¬p₂)∧(¬p₁→ p₁)∧(¬p₂→(p₃∨p₄))

(b) (_p1∨ ¬p2)∧(_p2∨p3)∧(¬p3∨ ¬p4)∧(¬p1∨ ¬p2∨p3∨p4)

Exercise 9.2 Use theALC-Elimalgorithm to decide satisfiability of (a) the concept nameAw.r.t.T ={Av ∃r.A, > vA, ∀r.Av ∃r.A}. (b) the concept∀r.∀r.¬Bw.r.t.T ={¬AvB, Av ¬B, > v ¬∀r.A}.

Give the constructed type sequenceΓ0,Γ1, . . .. In case of satisfiability, also give the satisfying model constructed in the proof of Lemma 5.10.

Exercise 9.3 Extend theALC-Elimalgorithm to the description logicALCI. Prove the correctness of the extended algorithm.

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