Reasoning with Rules SWRL as Example Jan Pettersen Nytun, UIA 1 - - PowerPoint PPT Presentation

Reasoning with Rules

SWRL as Example

Jan Pettersen Nytun, UIA

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What is a rule?

• Consist of premise and a conclusion.
• Meaning: In any situation where the premise

applies the conclusion must also hold.

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premise  conclusion

Agenda

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Different Types of Reasoning

• Inductive reasoning
• Deductive reasoning
• Abductive reasoning

 Why rules?  The Semantic Web Rule Language (SWRL)  SWRL Types of Atoms  SWRL Example  SWRL Exercise

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. …

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premise  conclusion

Not as strong as for deductive reasoning

S O P

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

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premise  conclusion

based on observations Likely to be true

Inductive Reasoning Example

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Many observations indicate that humans eventually dies, i.e., humans are mortals.

Human(x) Mortal(x)

Deductive Reasoning

also Called Deductive Logic, Logical Deduction

• 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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From Wikipedia, the free encyclopedia

Deductive Reasoning Example

All men are mortal. Socrates is a man.

• Therefore, Socrates is mortal.

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Deductive Reasoning Example in First Order Predicate Logic

All men are mortal. Socrates is a man.

• Therefore, Socrates is mortal.

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∀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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From Wikipedia, the free encyclopedia

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[https://explorable.com/inductive-reasoning]

Theories have to be tested and hypotheses answered before the scientific community accepts them as truth.

Abductive Reasoning

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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.

From Wikipedia, the free encyclopedia

RaindLastNight GrassIsWeet SprinklerWasOn GrassIsWeet

• 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.

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Abductive Reasoning Continues…

RaindLastNight GrassIsWeet SprinklerWasOn  GrassIsWeet

• 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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Abductive Reasoning Example

ref.: https://www.quora.com/What-is-a-good-example-of-abductive-reasoning

Agenda

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Different Types of Reasoning

• Inductive reasoning
• Deductive reasoning
• Abductive reasoning

 Why rules?  The Semantic Web Rule Language (SWRL)  SWRL Types of Atoms  SWRL Example  SWRL Exercise

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In some cases we need both Structure and Rules

Knowledge Representation, Part II, JPN, UiA 18

hasParent(?x,?parent) ∧ hasBrother(?parent,?uncle) ⇒ hasUncle(?x,?uncle)

Example of rule using The Semantic Web Rule Language (SWRL):

• Some statements cannot

be expressed in OWL.

• Modeling constructs of

OWL not always adequate or most desirable.

Agenda

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Different Types of Reasoning

• Inductive reasoning
• Deductive reasoning
• Abductive reasoning

 Why rules?  The Semantic Web Rule Language (SWRL)  SWRL Types of Atoms  SWRL Example  SWRL Exercise

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Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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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atom ^ atom .... → atom ^ atom

SWRL Rule

head body body and head consist of positive conjunctions of atoms (only AND between atoms)

p(arg1, arg2, ... argn)

p is a predicate symbol; arg1, arg2, ..., argn are the terms of the expression.

Atom

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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All variables in SWRL are treated as universally quantified (), with their scope limited to a given rule.

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ hasParent(?x,?parent) ∧ hasBrother(?parent,?uncle) ⇒ hasUncle(?x,?uncle)

E.g., given: This rule applies for all ?x, all ?parent and all ?uncle.

Agenda

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Different Types of Reasoning

• Inductive reasoning
• Deductive reasoning
• Abductive reasoning

 Why rules?  The Semantic Web Rule Language (SWRL)  SWRL Types of Atoms  SWRL Example  SWRL Exercise

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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

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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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)

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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(hasChild >= 1)(?x) -> Parent(?x) Example of Class Expression

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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)

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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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)

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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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)

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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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.

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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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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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)

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

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Rectangle(?r) ^ hasWidthInMeters(?r, ?w) ^ hasHeightInMeters(?r, ?h) ^ swrlb:multiply(?areaInSquareMeters, ?w, ?h)  hasAreaInSquareMeters(?r, ?areaInSquareMeters)

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ

Agenda

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Different Types of Reasoning

• Inductive reasoning
• Deductive reasoning
• Abductive reasoning

 Why rules?  The Semantic Web Rule Language (SWRL)  SWRL Types of Atoms  SWRL Example  SWRL Exercise

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Description Logic: Person and authorOf some Book

Example:

If a person is the author of a book then she is a (member of the class) book author.

DL and SWRL has a big overlap

First Order Predicate Logic: ∀x.Person(x) ∧ ∃y.authorOf(x,y) ∧ Book(y) →Bookauthor(x) SWRL: Person(?x) ^ authorOf(?x, ?y) ^Book(?y) -> BookAuthor(?x)

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Example in Protégé

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:authorOf rdf:type owl:ObjectProperty . :Book rdf:type owl:Class . :Person rdf:type owl:Class . :BookAuthor rdf:type owl:Class ;

• wl:equivalentClass

[ owl:intersectionOf ( :Person [ rdf:type owl:Restriction ;

• wl:onProperty :authorOf ;
• wl: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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DL reasoner infer that ibsen is a book author

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Make SWRL rule in Protégé

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Transfer SWRL rule to rule engine

After pressing

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Run SWRL rule

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See result of reasoning

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Result of SWRL reasoning

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Different Types of Reasoning

• Inductive reasoning
• Deductive reasoning
• Abductive reasoning

 Why rules?  The Semantic Web Rule Language (SWRL)  SWRL Types of Atoms  SWRL Example  SWRL Exercise

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Exercise this ontology is given

• wl:onProperty :contains ;
• wl:someValuesFrom :SalmonProduct

• wl:onProperty :contains ;
• wl:someValuesFrom :Chickpeas

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Ontology loaded into Protégé

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Even if no rule is specified the inference engine will still do some inferencing:

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“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.:

Task 1:

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(1)“Every vegetarian dislikes all fish products.”

Vegetarian(?x) ^ FishProduct(?y) -> dislikes(?x, ?y)

Task 1 Solution:

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“Anyone who ordered a dish that contains something he

• r she dislikes is unhappy.”

Task 2:

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“Anyone who ordered a dish that contains something he

• r she dislikes is unhappy.”

Task 2 solution:

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“Everything that can be ordered as a dish actually is a dish.”

Task 3:

Add the following to test:

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“Everything that can be ordered as a dish actually is a dish.”

Task Solution 3:

References

Jan Pettersen Nytun, UiA, page 58

Foundations of Semantic Web Technologies, Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph, Chapman & Hall/CRC, 2009

http://www.powershow.com/view4/5a7f2a- OGRlM/SWRL_Semantic_Web_Rule_Language_powerpoint_ppt_presentation

Help SWRL Protégé 5: https://github.com/protegeproject/swrlapi/wiki