Question 1
The given rule states that all entities connected to a trilogy using the property has are of type Volume, so only volumes can be linked to trilogies by that property.
Question 2
If to classes are equivalent then they share the same set of instances. This also means that all instances of the one class are also instance of the superclasses of the other.
It is not necessary that the classes have instances at all and of course if one class is empty the other is also empty. Since it is not required that instances of a class need to be instance of a subclass, that is also not required for equivalent classes.
Question 3
In the lecture we saw various possibilities to define the disjointness of classes:
:Novel owl:disjointWith :Poem .
[] a owl:AllDisjointClasses; owl:members ( :Novel :Poem ) .
:Novel rdfs:subClassOf [ owl:complementOf :Poem ] .
Question 4
It might have been confusing, that only one answer was allowed here, actually that was not intended. But only one answer was correct, which might have helped on the other hand:
It is a clause: disjunction of atomic formulas or negated atomic formulas.
It is no horn clause: clause with at most one not negated atom.
It is no definite clause: clause with exactly one not negated atom.
It is no fact: clause of a single not negated atom.
Question 5
To guarantee decidability in SHROIQ(D) only simple properties are allowed for number restrictions. Simple properties are
- properties that are not directly or indirectly dependent of property chains,
- properties that are not on the right side of a property inclusion R ○ T ⊑ S, and
- properties that are the inverse of other simple properties.
The remaining to options were false and actually stated the same: to be directly or indirectly dependent of property chains.
Question 6
Two options allow to restrict a person to have only one father: making :father a functional property or introducing a cardinality restriction on the :Person class.
One could say, that is not sufficient, because doing so makes :Alex and :Stefan one person. A reasoner would deduce the fact
:Alex owl:sameAs :Stefan .Well, nothing speaks against it! Possibly they are, there will be no conflict in the knowledge as long as we know they are distinct, e.g. because it is explicitly stated or they have different social security numbers (which might be an inverse functional property).
Question 7
The correct translation to DL was
FifaWorldCup ≡ Competition ⊓ (=32)participant ⊓ ∀participant.NationalSoccerTeam ⊓ sport.(Soccer)
FifaWorldCup is a subclass of Competition with three restrictions (1) there are exactly 32 participants, (2) all participants are of class NationalSoccerTeam, and (3) the performed sport is soccer.
Question 8
A functional property allows only one entity to be linked to another entity. So, if dbo:birthPlace would be a functional property, Athens would become identical to Greece, because both are listed as Kapino's birthplace.