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

JPN, UiA 2

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 JPN, UiA 3

Agenda  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 4

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 JPN, UiA 5

Inductive Reasoning S O P 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 JPN, UiA 6

Inductive Reasoning Example Many observations indicate that humans eventually dies, i.e., humans are mortals. Human(x)  Mortal(x) JPN, UiA 7

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. JPN, UiA 8

Deductive Reasoning Example All men are mortal. Socrates is a man. ------------------------------ Therefore, Socrates is mortal. JPN, UiA 9

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 JPN, UiA 10

From Wikipedia, the free encyclopedia JPN, UiA 11

[https://explorable.com/inductive-reasoning] Theories have to be tested and hypotheses answered before the scientific community accepts them as truth. JPN, UiA 12

Abductive Reasoning 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. RaindLastNight  GrassIsWeet 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. SprinklerWasOn  GrassIsWeet JPN, UiA 13

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. RaindLastNight  GrassIsWeet SprinklerWasOn  GrassIsWeet • Can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. JPN, UiA 14

Abductive Reasoning Example ref.: https://www.quora.com/What-is-a-good-example-of-abductive-reasoning • 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. JPN, UiA 15

In some cases we need both Structure and Rules JPN, UiA 17

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 18

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. JPN, UiA 20

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ 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. JPN, UiA 21

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ 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 22

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ 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 JPN, UiA 24

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) JPN, UiA 25

Example of Class Expression (hasChild >= 1)(?x) -> Parent(?x) JPN, UiA 26

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ 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) JPN, UiA 27

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) JPN, UiA 28

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ 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) JPN, UiA 29

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. JPN, UiA 30

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) JPN, UiA 31

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ 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 32

Ref.: https://github.com/protegeproject/swrlapi/wiki/SWRLLanguageFAQ Rectangle(?r) ^ hasWidthInMeters(?r, ?w) ^ hasHeightInMeters(?r, ?h) ^ swrlb:multiply(?areaInSquareMeters, ?w, ?h)  hasAreaInSquareMeters(?r, ?areaInSquareMeters) JPN, UiA 33

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

Reasoning with Rules SWRL as Example Jan Pettersen Nytun, UIA 1 JPN, UiA 2 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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