Musterlösung zu Aufgabe 3.8

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The triple rdf:type rdfs:range rdfs:Class . is an axiomatic triple of RDFS and can thus be derived using the RDFS semantics. However, OWL DL does not allow us to use rdfs:Class; hence this statement cannot be derived using the OWL DL semantics.

The triple r rdfs:domain B . cannot be derived from the RDFS semantics. There is no easy way to check this, but you can exhaustively apply all deduction rules and then this triple will not be included. In DL syntax the triple becomes \exists r.\top \sqsubseteq B, which is a logical consequence of the two given statements. To see this, let I be an arbitrarily chosen model for the two given statements. Then, using the definition of model and the two given statements, we obtain (\exists r.\top)^I \subseteq A^I \subseteq B^I, which shows that (\exists r.\top)^I \subseteq B^I. Hence \exists r.\top \sqsubseteq B holds in I, and since I was an arbitrarily chosen model, \exists r.\top \sqsubseteq B holds in all models for the two given statements, and thus is a logical consequence from these two statements.

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