How to infer isBrotherOf property between two individuals

Question

I need to infer that one individual is the brother of other one if they have the same father.

So, if I have this:

Bart hasFather Homer.

Lisa hasFather Homer.

Because Bart and Lisa have the same father, I would like to infer:

Lisa hasBrother Bart.

Is there any method to do that using any property characteristics?

Egest

A shame that a situation that intuitive and common has such an overcomplicated representation in OWL... – Boak

@Boak It's less complicated if other properties have been defined. For instance, if Ortzi had used, instead, Homer hasSon Bart, and Homer hasDaugher Lisa, and declared that hasSon and hasDaughter are subproperties of hasChild, and defined hasParent as an inverse to hasChild, then hasBrother would just be hasParent o hasSon. (That wouldn't handle the man is his own brother issue, though.) The complexity of the solution depends on the expressiveness of the existing representation. (Maybe I should add this to my answer…) – Laodicea

Answer 1

Use Property Chains and Rolification

Antoine Zimmermann's answer is a very good start to this problem, and touches on the major point that you need to solve this sort of task:

From x to each of x's brothers, there is a path of the form hasFather o hasFather^-1.

Now, that's actually not true of just brothers, though. That's true for all siblings and for x itself. This means you'll have the following definition of hasSibling:

hasSibling ≡ hasFather o hasFather^-1

(Actually, that's really just hasPaternalSibling; a more refined definition would use hasParent.) Now, using this, you could ask for brothers, which are simply siblings who are men, of x with a query like:

(hasSibling value x) and Man

However, it would be nice to define a proper hasBrother property. You could do this with a property chain and hasSibling if you had a special property that linked each Man to himself, and only linked males to themselves:

hasBrother ≡ hasSibling o specialProperty

In fact, such a property is what we get from a technique called rolification, which has been described more in a question, OWL 2 rolification, and its answer. The idea is that for the class Man, we create a new property r_Man and add the equivalence:

Man ≡ r_Man some Self

which says that each Man is related to himself by the r_Man property, and that only instances of Man are so connected. This is exactly the property that we need as specialProperty above. Thus, we end up with the following definitions of Man, hasSibling, and hasBrother:

Now we can ask for the brothers of x with a query like:

hasBrother^-1 value x

For instance, we can ask for Greg's siblings, and get Peter, Greg (himself), and Bobby.

Sample Ontology

Here's that ontology in Turtle:

@prefix :      <http://www.example.org/brady#> .
@prefix rdfs:  <http://www.w3.org/2000/01/rdf-schema#> .
@prefix brady: <http://www.example.org/brady#> .
@prefix owl:   <http://www.w3.org/2002/07/owl#> .
@prefix xsd:   <http://www.w3.org/2001/XMLSchema#> .
@prefix rdf:   <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .

brady:hasSibling  a             owl:ObjectProperty ;
        owl:propertyChainAxiom  ( brady:hasFather [ owl:inverseOf
                          brady:hasFather ] ) .

brady:Carol  a  owl:NamedIndividual , brady:Woman .

brady:hasBrother  a             owl:ObjectProperty ;
        owl:propertyChainAxiom  ( brady:hasSibling brady:r_Man ) .

<http://www.example.org/brady>
        a       owl:Ontology .

brady:Woman  a               owl:Class ;
        rdfs:subClassOf      brady:Person ;
        owl:equivalentClass  [ a               owl:Restriction ;
                               owl:hasSelf     true ;
                               owl:onProperty  brady:r_Woman
                             ] .

brady:hasFather  a  owl:ObjectProperty .

brady:Person  a  owl:Class .

brady:Man  a                 owl:Class ;
        rdfs:subClassOf      brady:Person ;
        owl:equivalentClass  [ a               owl:Restriction ;
                               owl:hasSelf     true ;
                               owl:onProperty  brady:r_Man
                             ] .

brady:r_Woman  a  owl:ObjectProperty .

brady:r_Man  a  owl:ObjectProperty .

brady:Marcia  a          owl:NamedIndividual , brady:Woman ;
        brady:hasFather  brady:Mike .

brady:Peter  a           owl:NamedIndividual , brady:Man ;
        brady:hasFather  brady:Mike .

brady:Jan  a             owl:NamedIndividual , brady:Woman ;
        brady:hasFather  brady:Mike .

brady:Cindy  a           owl:NamedIndividual , brady:Woman ;
        brady:hasFather  brady:Mike .

brady:Bobby  a           owl:NamedIndividual , brady:Man ;
        brady:hasFather  brady:Mike .

brady:Greg  a            owl:NamedIndividual , brady:Man ;
        brady:hasFather  brady:Mike .

brady:Mike  a   owl:NamedIndividual , brady:Man .

Laodicea

Unbelievable answer! Thanks. – Egest

I have a question about the answer. In that solution, if we have two brothers A and B, the infered result shows that A hasSibling B, but also shows that A hasSibling A. Could it be solved? – Bianca

@Bianca That's a good observation, and there aren't very good solutions to work around it, unfortunately. Depending on your use case, the best thing might just be to filter out those results. E.g., see the comments on AntoineZimmermann's answer. – Laodicea

what is an "o" here in this statement ? "hasFather o inverse (hasFather)" – Octangular

@Octangular It's property composition, or a property chain, in OWL terminology. E.g., if Joe fatherOf Tim and Tim brotherOf Hank, then Joe fatherOf o brotherOf Hank. In the Manchester syntax (that Protege uses), you input it with just a lowercase letter "o". – Laodicea

Answer 2

Assuming that everyone is their own brother, and that sisters are brothers too:

:hasBrother  owl:propertyChainAxiom  (:hasFather [ owl:inverseOf :hasFather ]) .

It is hardly possible to define :hasBrother more precisely, excluding female brothers and self-brotherhood. But you can infer all the brothers of Lisa as follows:

:Female  a  owl:Class .
:Male  a  owl:Class;
  owl:disjointWith  :Female .
:Lisa  a  :Female .
:Bart  a  :Male .
:Homer a  :Male .
:hasFather  a  owl:ObjectProperty;
  rdfs:range  :Male .
:hasBrother a  owl:ObjectProperty;
  rdfs:range  :Male .
:hasSiblingOrSelf  owl:propertyChainAxiom  ( :hasFather [ :hasFather ] ) .
:LisaBrother  owl:equivalentClass  [
    a  owl:Restriction;
    owl:onProperty  [ owl:inverseOf  :hasBrother ];
    owl:hasValue  :Lisa
  ], [
    a  owl:Class;
    owl:intersectionOf  (
      [ a owl:Restriction; owl:onProperty :hasSiblingOrSelf; owl:hasValue :Lisa ]
      :Male
    )
  ] .

Reptant

Using rolification and a Female class, I think you could actually exclude sisters pretty easily. I'm not sure whether you could easily exclude self-brothers, though. – Laodicea

Yes, you're right. The last hard thing is to exclude being brother of oneself. I don't know how to do it if it is at all possible, in OWL. – Reptant

Answer 3

One way to this is by using SWRL rules.

On protege:

1. go to Window
2. Click on Tabs
3. Click on Swrl Tab
4. Press the "new" button and write the following rule

Write rule:

isChildOf(?x,?y)^FatherOf(?y,?z)^differentFrom(?z,?x)->isBrotherOf(?x,?z)

This means that if "x is a child of y", and "y is also a parent of z" and "z and x are different" then "z and x are Brothers".

Phyllisphylloclade

Answer 4

A brother is a male sibling. Consequently, we should define both 'male' and being a sibling. But since a sibling is itself a non-identical child of the same parents, one should also define being a child. For simplicity, we'll treat half-siblings as siblings, restrict the domain to humans, and leave the explicit definition of related concepts like motherhood and fatherhood aside.

1 Define Man

1. Create a Human class
2. Create a Gender class disjoint with the Human class. Create male and female as individuals instantiating the Gender type (there are other ways to do this, but this is a pretty simple one).
3. Create a hasGender Object property, with Human as domain and Gender for its range
4. Create a Man class as a subclass of Human. Make it equivalent to Human and (hasGender value male).

2 Define child

5. Create an isChildOf Object property with Human for both its domain and range (Optional: Define a Child class as a subtype of human equivalent to isChildOf some Human. In similar fashion, you can also create object properties, then classes for Mother, Parent, Daughter, etc).

3 Define sibling with help from SWRL

6. First, create an irreflexive, symmetric isSiblingOf object property in Protege with Human for its domain and range.
7. In the menu bar at the top of Protege, ensure Window -> tabs -> SWRLTab is checked and then find and click on the SWRLTab tab.
8. Click new to create a new rule, and add the rule: isChildOf(?sibling1, ?parent) ^ isChildOf(?sibling2, ?parent) ^ differentFrom(?sibling1, ?sibling2) -> isSiblingOf(?sibling1, ?sibling2) You may also want to add rules for what you want to be able to infer from the siblinghood relation, e.g isSiblingOf(?x, ?y) ^ isChildOf(?x, z?) -> isChildOf(?y, ?z)

4 Define being a brother of

9. Create an isBrotherOf Object property in Protege with domain Man and range Human
10. On the SWRLTab, add the following rules: Man(?x) ^ isSiblingOf(?x, ?y) -> isBrotherOf(?x, ?y)

isBrotherOf(?x, ?y) -> Man(?x)

isBrotherOf(?x, ?y) -> isSiblingOf(?x, ?y)

The first rule states that any male sibling is a brother. The second and third infer maleness and siblinghood from brotherhood.

11. Optionally create a Brother class equivalent to isBrotherOf some Human to complete the rollification process.

Rattlebrain