Using OWL (The Web Ontology Language) to model a humorous variant of Einstein's riddle

1. 6’6’’
6’0’’
5’6’’
5’0’’
4’6’’
4’0’’
3’6’’
3’0’’
6’6’’
6’0’’
5’6’’
5’0’’
4’6’’
4’0’’
3’6’’
3’0’’
Who owns the
robot chicken?

2. Donald J. Trump
Dr. Evil
Kim Jong-un
Frank Underwood
Bane

3. Shark
Octopus
Tortoise
Armadillo
Robot
Chicken

7. 1. There are five houses.
2. Frank Underwood lives in the Red house.
3. Dr. Evil owns the frickin’ Octopus.
4. Whiskey is the preferred drink in the Black house.
5. Donald Trump drinks Bourbon.
6. The Black house is just to the right of the White house.
7. The Black Lung smoker owns the Tortoise.
8. French Soot is smoked in the Brown house.
9. Tequila is the preferred drink in the middle house.
10.Bane lives in the first house.
11.The villain who smokes Coal Dust lives in the house next
to the villain with the Armadillo.
12.French Soot is smoked in a house next to the house
where the Shark is kept.
13.The Slow Death smoker drinks Vodka.
14.Kim Jong-un smokes Hacking Cough.
15.Bane lives next to the Blue house.

8. Who owns the
robot chicken?
Who drinks
champagne?

9. @prefix : <http://ngrams.ucd.ie/hawking#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@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#> .
Every line is a
triple, ending
with a period.

10. Anonymous
classes are
defined in [ ]
<http://ngrams.ucd.ie/hawking> rdf:type owl:Ontology .
[ rdf:type owl:AllDisjointClasses ;
owl:members ( :Color :Drink :House :Person :Pet :Smoke ) ] .
Separate triples
with a semicolon

11. Let’s define the
key classes in
the riddle …
:Color rdf:type owl:Class ;
owl:equivalentClass
[ rdf:type owl:Class ;
owl:oneOf ( :Blue :Brown :White :Black :Red ) ] .
:Drink rdf:type owl:Class ;
owl:equivalentClass
[ rdf:type owl:Class ;
owl:oneOf ( :Vodka :Champagne :Bourbon :Tequila :Whiskey ) ] .

12. Now for
the relations
between classes
:drinks rdf:type owl:FunctionalProperty ,
owl:InverseFunctionalProperty ,
owl:ObjectProperty ;
rdfs:domain :Person;
rdfs:range :Drink .
:hasColor rdf:type owl:FunctionalProperty ,
owl:InverseFunctionalProperty ,
owl:ObjectProperty ;
rdfs:domain :House ;
rdfs:range :Color .
Use commas for
multiple values
for a property
But what’s an
inverse
functional
property?

13. owl:onProperty
owl:someValuesFrom
:Color
rdfs:subClassOf
:House rdf:type owl:Class ;
rdfs:subClassOf [
rdf:type owl:Restriction ;
owl:onProperty :hasColor ;
owl:someValuesFrom :Color ] .
:hasColor
owl:Restriction
owl:Class
rdf:type
???
rdf:type
:House

14. :Person rdf:type owl:Class ;
rdfs:subClassOf
[ rdf:type owl:Class ;
owl:intersectionOf (
[ rdf:type owl:Restriction ;
owl:onProperty :drinks ;
owl:someValuesFrom :Drink ]
[ rdf:type owl:Restriction ;
owl:onProperty :hasPet ;
owl:someValuesFrom :Pet ]
[ rdf:type owl:Restriction ;
owl:onProperty :livesIn ;
owl:someValuesFrom :House ]
[ rdf:type owl:Restriction ;
owl:onProperty :smokes ;
owl:someValuesFrom :Smoke ]
)
] .
Ensure every
person has all
of the vices …

15. :isNextTo rdf:type owl:IrreflexiveProperty ,
owl:ObjectProperty ,
owl:SymmetricProperty ;
rdfs:domain :House ;
rdfs:range :House .
:isRightTo rdf:type owl:FunctionalProperty ,
owl:InverseFunctionalProperty ,
owl:ObjectProperty ;
owl:inverseOf :isLeftTo ;
rdfs:subPropertyOf :isNextTo .
:isLeftTo rdf:type owl:ObjectProperty ;
rdfs:subPropertyOf :isNextTo .
Now to
constrain the
neighbours!

16. :House1 :isLeftTo :House2 .
:House2 :isLeftTo :House3 .
:House3 :isLeftTo :House4 .
:House4 :isLeftTo :House5 .
[ rdf:type owl:NegativePropertyAssertion ;
owl:assertionProperty :isNextTo ;
owl:targetIndividual :House1 ;
owl:sourceIndividual :House5 ] .
[ rdf:type owl:AllDifferent ;
owl:distinctMembers ( :House2 :House1 :House4 :House3 :House5 ) ] .

17. :House rdf:type owl:Class ;
rdfs:subClassOf
[ rdf:type owl:Restriction ;
owl:onProperty :isNextTo ;
owl:onClass :House ;
owl:maxQualifiedCardinality
"2"^^xsd:nonNegativeInteger ] ,
[ rdf:type owl:Restriction ;
owl:onProperty :hasColor ;
owl:someValuesFrom :Color ] .
Qualified
cardinality!
Eureka!
A house has
at most two
neighboring
houses
and at least
(but only)
one colour!

18. [ rdf:type owl:AllDifferent ;
owl:distinctMembers (:Black :White :Red :Brown :Blue) ] .
[ rdf:type owl:AllDifferent ;
owl:distinctMembers ( :DrEvil :Bane :FrankUnderwood
:DonaldTrump :KimJongUn ) ] .
[ rdf:type owl:AllDifferent ;
owl:distinctMembers ( :Bourbon :Vodka :Champagne :Whiskey
:Tequila ) ] .
[ rdf:type owl:AllDifferent ;
owl:distinctMembers ( :Octopus :RobotChicken :Armadillo :Tortoise
:Shark ) ] .
[ rdf:type owl:AllDifferent ;
owl:distinctMembers ( :BlackLung :FrenchSoot :CoalDust :SlowDeath
:HackingCough ) ] .
I’m no
Einstein, but
I could be!
So beware the
non-unique names
assumption

19. :FrankUnderwood :livesIn [ :hasColor :Red ] .
:DrEvil :hasPet :Octopus .
[] :drinks :Whiskey ;
:livesIn [ :hasColor :Black ] .
:DonaldTrump :drinks :Bourbon .
[] :hasColor :Black ;
:isRightTo [ :hasColor :White ] .
[] :smokes :BlackLung ;
:hasPet :Tortoise .
Now for the
specific facts of the
riddle …
[ ] denotes a
blank node

20. [] :drinks :Whiskey ;
:livesIn [ :hasColor :Black ] .

21. }
[] :smokes :FrenchSoot ;
:livesIn [ :hasColor :Brown ] .
[] :drinks :Tequila ;
:livesIn :House3 .
:Bane :livesIn :House1 .
[] :smokes :CoalDust ;
:livesIn [ :isNextTo _:x11 ] .
[] :livesIn _:x11 ;
:hasPet :Armadillo .

22. [] :livesIn _:x11 ;
:hasPet :Armadillo .
[] :smokes :CoalDust ;
:livesIn [ :isNextTo _:x11 ] .

23. [] :smokes :FrenchSoot;
:livesIn [ :isNextTo _:x12 ] .
[] :livesIn _:x12 ;
:hasPet :Shark .
[] :smokes :SlowDeath ;
:drinks :Vodka .
:KimJongUn :smokes :HackingCough .
:Bane :livesIn [ :isNextTo [ :hasColor :Blue ] ] .
}

27. French
Soot

28. French
Soot

29. French
Soot Slow
Death
Hacking
Cough

30. Slow
Death
Hacking
Cough
Black
Lung
Coal
Dust
French
Soot

36. Hawking:
The Riddle
Credits
Hawking’s riddle is based on “Einstein’s Riddle” from Life
magazine in December, 1962. Einstein’s connection to the
riddle is apocryphal, and about as tenuous as Hawking’s.
My solution here is based on that of Martin G. Skjæveland