1. Reasoning with Rules SWRL as Example
Jan Pettersen Nytun, UIA

2. JPN, UiA

3. premise  conclusion What is a rule?
Consist of premise and a conclusion.
Meaning: In any situation where the premise applies the conclusion must also hold.
premise  conclusion
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4. Agenda Different Types of Reasoning Why rules?
Inductive reasoning
Deductive reasoning
Abductive reasoning
Why rules?
The Semantic Web Rule Language (SWRL)
SWRL Types of Atoms
SWRL Example
SWRL Exercise

5. Inductive Reasoning From Wikipedia, the free encyclopedia
…the premises are viewed as supplying strong evidence for the truth of the conclusion. … conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument is probable, based upon the evidence given. …
premise  conclusion
Not as strong as for deductive reasoning
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6. Inductive Reasoning From Wikipedia, the free encyclopedia
…the premises of an inductive logical argument indicate some degree of support for the conclusion but do not entail it... derives general principles from specific observations
based on observations
premise  conclusion
Likely to be true
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7. Inductive Reasoning Example
Many observations indicate that humans eventually dies, i.e., humans are mortals.
Human(x) Mortal(x)
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8. Deductive Reasoning also Called Deductive Logic, Logical Deduction
From Wikipedia, the free encyclopedia
If all premises are true, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.
In inductive reasoning, the conclusion is reached by generalizing or extrapolating from specific cases to general rules, i.e., there is … uncertainty.
However, induction used in mathematical proofs is actually a form of deductive reasoning.
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9. Deductive Reasoning Example
All men are mortal. Socrates is a man Therefore, Socrates is mortal.
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10. Deductive Reasoning Example in First Order Predicate Logic
All men are mortal. Socrates is a man Therefore, Socrates is mortal.
∀x.Man(x)  Mortal(x) All men are mortal
Man(Socrates) Socrates is a man
Man(Socrates)  Mortal(Socrates). -- Socrates is mortal
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11. From Wikipedia, the free encyclopedia
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12. [https://explorable.com/inductive-reasoning]
Theories have to be tested and hypotheses answered before the scientific community accepts them as truth.
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13. Abductive Reasoning RaindLastNight GrassIsWeet
From Wikipedia, the free encyclopedia
Example: The grass is wet; if it rained last night, then it would be unsurprising that the grass is wet. Therefore, by abductive reasoning, the possibility that it rained last night is reasonable.
Some other process could have also resulted in a wet grass, such as sprinklers. Consequently, abducing that it rained last night from the observation of wet grass can lead to a false conclusion.
RaindLastNight GrassIsWeet
SprinklerWasOn GrassIsWeet
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14. Abductive Reasoning Continues…
Inference to the best explanation.
Given a true conclusion and a rule, it attempts to select some possible premises that, if true also, can support the conclusion, though not uniquely.
Can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data.
RaindLastNight GrassIsWeet
SprinklerWasOn  GrassIsWeet
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15. Abductive Reasoning Example ref. : https://www. quora
The doctor hears her patients symptoms, including the regular shortness of breath on cold days and when exercising and abduces that the best explanation of these symptoms is that her patient is an asthma sufferer.
The scientist observes the test tube and sees the chemical turn purple. She abduces that either there is potassium in the sample or her colleague is playing yet another prank on her.
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16. Agenda Different Types of Reasoning Why rules?
Inductive reasoning
Deductive reasoning
Abductive reasoning
Why rules?
The Semantic Web Rule Language (SWRL)
SWRL Types of Atoms
SWRL Example
SWRL Exercise

17. In some cases we need both Structure and Rules
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18. Knowledge Representation, Part II, JPN, UiA
Example of rule using The Semantic Web Rule Language (SWRL): 
hasParent(?x,?parent) ∧ hasBrother(?parent,?uncle)
⇒ hasUncle(?x,?uncle)
Some statements cannot be expressed in OWL.
Modeling constructs of OWL not always adequate or most desirable.
Knowledge Representation, Part II, JPN, UiA

19. Agenda Different Types of Reasoning Why rules?
Inductive reasoning
Deductive reasoning
Abductive reasoning
Why rules?
The Semantic Web Rule Language (SWRL)
SWRL Types of Atoms
SWRL Example
SWRL Exercise

20. The Semantic Web Rule Language (SWRL)
Ref.:
The Semantic Web Rule Language (SWRL)
An expressive OWL-based rule language.
SWRL allows users to write rules that can be expressed in terms of OWL concepts to provide more powerful deductive reasoning capabilities than OWL alone.
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21. SWRL Rule Atom p(arg1, arg2, ... argn) head body
Ref.:
SWRL Rule
head
body
atom ^ atom .... → atom ^ atom
body and head consist of positive conjunctions of atoms (only AND between atoms)
Atom
p(arg1, arg2, ... argn)
p is a predicate symbol; arg1, arg2, ..., argn are the terms of the expression.
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22. This rule applies for all ?x, all ?parent and all ?uncle.
Ref.:
All variables in SWRL are treated as universally quantified (), with their scope limited to a given rule.
E.g., given:
hasParent(?x,?parent) ∧ hasBrother(?parent,?uncle)
⇒ hasUncle(?x,?uncle)
This rule applies for all ?x, all ?parent and all ?uncle.
JPN, UiA

23. Agenda Different Types of Reasoning Why rules?
Inductive reasoning
Deductive reasoning
Abductive reasoning
Why rules?
The Semantic Web Rule Language (SWRL)
SWRL Types of Atoms
SWRL Example
SWRL Exercise

24. SWRL provides seven types of atoms:
Ref.:
SWRL provides seven types of atoms:
Class Atoms
Individual Property atoms
Data Valued Property atoms
Different Individuals atoms
Same Individual atoms
Built-in atoms
Data Range atoms
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25. Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ
Class Atom OWL named class or class expression and a single argument representing an OWL individual
Examples:
Person(?p) Man(Fred)
Man(?p) -> Person(?p)
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26. Example of Class Expression
(hasChild >= 1)(?x) -> Parent(?x)
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27. Individual Property Atom
Ref.:
Individual Property Atom
OWL object property and two arguments
representing OWL individuals. Examples:
hasBrother(?x, ?y) hasSibling(Fred, ?y)
Person(?p) ^ hasSibling(?p,?s) ^ Man(?s) -> hasBrother(?p,?s)
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28. Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ
Data Valued Property
OWL data property and two arguments, the first representing an OWL individual, and the second a data value.
Examples:
hasAge(?x, ?age) hasHeight(Fred, ?h)
hasAge(?x, 232)
hasName(?x, "Fred")
Person(?p) ^ hasCar(?p, true) -> Driver(?p)
Person(Fred) ^ hasCar(Fred, true) -> Driver(Fred)
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29. Different Individuals Atom
Ref.:
Different Individuals Atom
Arguments representing OWL individuals.
Examples:
differentFrom(?x, ?y) differentFrom(Fred, Joe)
Same Individual Atom
Arguments representing OWL individuals.
Examples:
sameAs(?x, ?y)
sameAs(Fred, Freddy)
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30. Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ
Data Range Atom
A datatype name or a set of literals and a single argument representing a data value. Examples:
xsd:int(?x)
[3, 4, 5](?x)
?x is a variable representing a data value.
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31. Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ
Built-In Atom
SWRL support user-defined built-ins. A built-in is a predicate that takes one or more arguments and evaluates to true if the arguments satisfy the predicate.
SWRL contained many built-ins.
Example - Person with an age of greater than 17 is an adult is: :
Person(?p) ^ hasAge(?p, ?age) ^ swrlb:greaterThan(?age, 17) -> Adult(?p)
(swrlb is a namespace)
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32. Person(?p) ^ hasNumber(?p, ?number) ^ swrlb:startsWith(?number, "+")
Ref.:
A rule that uses a core SWRL string built-in to determine if a person's telephone number starts with the international access code "+" can be written as follows:
Person(?p) ^ hasNumber(?p, ?number) ^ swrlb:startsWith(?number, "+")
 hasInternationalNumber(?p, true)
JPN, UiA

33. hasWidthInMeters(?r, ?w) ^ hasHeightInMeters(?r, ?h) ^
Ref.:
Rectangle(?r) ^
hasWidthInMeters(?r, ?w) ^
hasHeightInMeters(?r, ?h) ^
swrlb:multiply(?areaInSquareMeters, ?w, ?h) 
hasAreaInSquareMeters(?r, ?areaInSquareMeters)
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34. Agenda Different Types of Reasoning Why rules?
Inductive reasoning
Deductive reasoning
Abductive reasoning
Why rules?
The Semantic Web Rule Language (SWRL)
SWRL Types of Atoms
SWRL Example
SWRL Exercise

35. DL and SWRL has a big overlap
Example: If a person is the author of a book then she is a (member of the class) book author.
First Order Predicate Logic:
∀x.Person(x) ∧ ∃y.authorOf(x,y) ∧ Book(y) →Bookauthor(x)
Description Logic:
Person and authorOf some Book
SWRL:
Person(?x) ^ authorOf(?x, ?y) ^Book(?y) -> BookAuthor(?x)
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36. Example in Protégé
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37. Ontology Used :authorOf rdf:type owl:ObjectProperty .
:Book rdf:type owl:Class .
:Person rdf:type owl:Class .
:BookAuthor rdf:type owl:Class ;
owl:equivalentClass
[ owl:intersectionOf
( :Person [ rdf:type owl:Restriction ; owl:onProperty :authorOf ; owl:someValuesFrom :Book ]
) ;
rdf:type owl:Class
] .
:aDollsHouse rdf:type owl:NamedIndividual , :Book .
:ibsen rdf:type owl:NamedIndividual , :Person ;
:authorOf :aDollsHouse , :peerGynt .
:notAnAuthorPerson rdf:type owl:NamedIndividual , :Person .
:peerGynt rdf:type owl:NamedIndividual , :Book .
Ontology Used
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38. DL reasoner infer that ibsen is a book author
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39. Make SWRL rule in Protégé
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40. JPN, UiA

41. Transfer SWRL rule to rule engine
After pressing
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42. Run SWRL rule
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43. See result of reasoning
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44. Result of SWRL reasoning
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45. Agenda Different Types of Reasoning Why rules?
Inductive reasoning
Deductive reasoning
Abductive reasoning
Why rules?
The Semantic Web Rule Language (SWRL)
SWRL Types of Atoms
SWRL Example
SWRL Exercise

46. Exercise this ontology is given
@prefix : < .
@prefix owl: < .
@prefix xsd: < .
@prefix xml: < .
@prefix rdf: < .
@base < .
@prefix rdfs: < .
< rdf:type owl:Ontology .
# Object Properties
#################################################################
:contains rdf:type owl:ObjectProperty .
###
:dislikes rdf:type owl:ObjectProperty .
###
:ordered rdf:type owl:ObjectProperty .
###
# Classes
###
[ rdf:type owl:Restriction ;
rdfs:subClassOf :Dish ,
:BakedSalmon rdf:type owl:Class ;
] .
owl:someValuesFrom :SalmonProduct
owl:onProperty :contains ;
:Chickpeas rdf:type owl:Class ;
###
rdfs:subClassOf :VeggiProduct .
:Dish rdf:type owl:Class .
###
:Falafel rdf:type owl:Class ;
###
owl:someValuesFrom :Chickpeas
rdfs:subClassOf :Product .
:FishProduct rdf:type owl:Class ;
###
:Person rdf:type owl:Class .
###
###
:Product rdf:type owl:Class .
:SalmonProduct rdf:type owl:Class ;
###
rdfs:subClassOf :FishProduct .
:Unhappy rdf:type owl:Class .
###
:Vegetarian rdf:type owl:Class .
###
:VeggiProduct rdf:type owl:Class ;
###
# Individuals
:Chickpeas .
:chickpeas1 rdf:type owl:NamedIndividual ,
###
:dish1BakedSalmon rdf:type owl:NamedIndividual ,
###
:contains :salmon1 .
:BakedSalmon ;
:disk2BakedSalmon rdf:type owl:NamedIndividual ,
###
:contains :salmon2 .
:disk3Falafel rdf:type owl:NamedIndividual ,
###
:Falafel ;
:contains :chickpeas1 .
:Person ;
:janeNotVeggi rdf:type owl:NamedIndividual ,
###
:ordered :dish1BakedSalmon .
###
:SalmonProduct .
:salmon1 rdf:type owl:NamedIndividual ,
:salmon2 rdf:type owl:NamedIndividual ,
###
:Person ,
:tomVeggi rdf:type owl:NamedIndividual ,
###
:disk3Falafel .
:ordered :disk2BakedSalmon ,
:Vegetarian ;
### Generated by the OWL API (version )
Exercise this ontology is given
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47. Ontology loaded into Protégé
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48. JPN, UiA

49. JPN, UiA

50. JPN, UiA

51. Even if no rule is specified the inference engine will still do some inferencing:
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52. Task 1: “Every vegetarian dislikes all fish products.”
In effect all individuals of type Vegetarian will dislike all individuals of type FishProduct (and all its subclasses).
E.g.:
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53. Task 1 Solution: “Every vegetarian dislikes all fish products.”
Vegetarian(?x) ^ FishProduct(?y) -> dislikes(?x, ?y)
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54. Task 2:
“Anyone who ordered a dish that contains something he or she dislikes is unhappy.”
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55. Task 2 solution:
“Anyone who ordered a dish that contains something he or she dislikes is unhappy.”
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56. Task 3: “Everything that can be ordered as a dish actually is a dish.”
Add the following to test:
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57. Task Solution 3:
“Everything that can be ordered as a dish actually is a dish.”
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58. References
Foundations of Semantic Web Technologies, Pascal Hitzler,  Markus Krötzsch,  Sebastian Rudolph, Chapman & Hall/CRC, 2009
Help SWRL Protégé 5: