Inverse property with range restriction - owl

Question

In Protege, I have defined a class :Person, and an object property :likes (with domain :Person and range :Person).
I have defined an inverse property of :likes called :isLikedBy.
Then I define an additional class :Rich.
I wish I could define a property :likesBackForBadReasons in this way: an equivalent property (or is it a subproperty?) of :isLikedBy, but only when the range of that relationship is an instance of :Rich.
So my inference engines infers that any :Rich :Person "A" who :likes a :Person "B", then this "B" :likesBackForBadReasons "A".
How to define that :likesBackForBadReasons object property in Protege?

Answer 1

TL;TDR: This specific requirement can only be dealt with using rules and not by typical Description Logic (DL) inferences. You can use either of the following rules:
Person(?x) ^ PersonThatIsNotRich(?x) ^ RichPerson(?y) ^ likes(?y, ?x) ^ likes(?x, ?y) -> BadPerson(?x)
Person(?x) ^ PersonThatIsNotRich(?x) ^ RichPerson(?y) ^ likes(?y, ?x) ^ likes(?x, ?y) -> likesForBadReason(?x, ?y)
where PersonThatIsNotRich is disjoint with RichPerson. These rules also ensure that a rich person liking another rich person will not be considered a bad person.
How to use SWRL to do this inference:
The ontology using this rule in Manchester syntax is as follows:
ObjectProperty: isLikedBy
InverseOf: likes
ObjectProperty: likes
InverseOf: isLikedBy
ObjectProperty: likesForBadReason
SubPropertyOf: likes
Class: BadPerson
SubClassOf: Person
Class: Person
Class: PersonThatIsNotRich
SubClassOf: Person
DisjointWith: RichPerson
Class: RichPerson
SubClassOf: Person
DisjointWith: PersonThatIsNotRich
Individual: badPerson
Types: Person
Facts: likes richPerson
Individual: otherBadPerson
Types: Person
Facts: likes otherRichPerson
Individual: otherRichPerson
Types: RichPerson
Facts: likes badPerson, likes richPerson
Individual: richPerson
Types: RichPerson
Facts: likes badPerson, likes otherRichPerson
Rule:
Person(?x), PersonThatIsNotRich(?x), RichPerson(?y), likes(?y, ?x), likes(?x, ?y) - BadPerson(?x)
Notes:
You will note that badPerson is inferred to be a BadPerson while otherBadPerson is not inferred to be a BadPerson. This is because otherBadPerson likes otherRichPerson, but otherRichPerson likes badPerson, not otherBadPerson. It is because the same rich person is not liked-back. It is the involvement of the same individual that causes a typical Description Logic reasoner to not be able to infer this correctly (or at least that is my understanding - someone who understands the difference between DL reasoners and rules better is welcome to correct me).
You will also note that a rich person liking another rich person and being liked back by that rich person, does not cause the rich person to be inferred to be a BadPerson.
Why intuitive solution using DL axiom does not work:
Intuitively one may think that defining BadPerson as follows will give the desired inference, but it does not:
Class: BadPerson
EquivalentTo:
(isLikedBy some RichPerson)
and (likes some Person) and (not RichPerson)
SubClassOf: Person
This will merely ensure that a BadPerson is liked by some rich person and that BadPerson likes some rich person, but the rich person is not necessarily the same rich person.
Why define a BadPerson class rather than a likesForBadReasons property in DL?
Reasoning in DL is defined in terms of classes and not in terms of relations. The basic reasoning in DL is classification and this aims to classify classes form the most general to the most specific. There is no such reasoning procedure for classification of relations.