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

Transcription

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

2 JPN, UiA 2

3 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

4 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

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 JPN, UiA 5

6 P S O 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 JPN, UiA 6

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

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. JPN, UiA 8

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

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 JPN, UiA 10

11 From Wikipedia, the free encyclopedia JPN, UiA 11

12 [ Theories have to be tested and hypotheses answered before the scientific community accepts them as truth. JPN, UiA 12

13 JPN, UiA 13 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

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. 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

15 Abductive Reasoning Example ref.: 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

16 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 16

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

18 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

19 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 19

20 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. JPN, UiA 20

21 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. JPN, UiA 21

22 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 22

23 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 23

24 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 JPN, UiA 24

25 Ref.: 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

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

27 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) JPN, UiA 27

28 Ref.: 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

29 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) JPN, UiA 29

30 Ref.: 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

31 Ref.: 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

32 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 32

33 Ref.: Rectangle(?r) ^ haswidthinmeters(?r,?w) ^ hasheightinmeters(?r,?h) ^ swrlb:multiply(?areainsquaremeters,?w,?h) hasareainsquaremeters(?r,?areainsquaremeters) JPN, UiA 33

34 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 34

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) JPN, UiA 35

36 Example in Protégé JPN, UiA 36

37 :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. Ontology Used :notanauthorperson rdf:type owl:namedindividual, :Person. :peergynt rdf:type owl:namedindividual, :Book. JPN, UiA 37

38 DL reasoner infer that ibsen is a book author JPN, UiA 38

39 Make SWRL rule in Protégé JPN, UiA 39

40 JPN, UiA 40

41 Transfer SWRL rule to rule engine After pressing JPN, UiA 41

42 Run SWRL rule JPN, UiA 42

43 See result of reasoning JPN, UiA 43

44 JPN, UiA 44 Result of SWRL reasoning

45 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 45

46 @prefix : owl: rdf: xml: xsd: rdfs: < < rdf:type owl:ontology. ################################################################# # Object Properties ################################################################# ### :contains rdf:type owl:objectproperty. ### :dislikes rdf:type owl:objectproperty. ### :ordered rdf:type owl:objectproperty. ################################################################# # Classes ################################################################# ### :BakedSalmon rdf:type owl:class ; rdfs:subclassof :Dish, [ rdf:type owl:restriction ; owl:onproperty :contains ; owl:somevaluesfrom :SalmonProduct ]. ### :Chickpeas rdf:type owl:class ; rdfs:subclassof :VeggiProduct. ### :Dish rdf:type owl:class. ### :Falafel rdf:type owl:class ; rdfs:subclassof :Dish, [ rdf:type owl:restriction ; owl:onproperty :contains ; owl:somevaluesfrom :Chickpeas ]. Exercise this ontology is given ### :FishProduct rdf:type owl:class ; rdfs:subclassof :Product. ### :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 ; rdfs:subclassof :Product. ################################################################# # Individuals ################################################################# ### :chickpeas1 rdf:type owl:namedindividual, :Chickpeas. ### :dish1bakedsalmon rdf:type owl:namedindividual, :BakedSalmon ; :contains :salmon1. ### :disk2bakedsalmon rdf:type owl:namedindividual, :BakedSalmon ; :contains :salmon2. ### :disk3falafel rdf:type owl:namedindividual, :Falafel ; :contains :chickpeas1. ### :janenotveggi rdf:type owl:namedindividual, :Person ; :ordered :dish1bakedsalmon. ### :salmon1 rdf:type owl:namedindividual, :SalmonProduct. ### :salmon2 rdf:type owl:namedindividual, :SalmonProduct. ### :tomveggi rdf:type owl:namedindividual, :Person, :Vegetarian ; :ordered :disk2bakedsalmon, :disk3falafel. ### Generated by the OWL API (version ) JPN, UiA 46

47 Ontology loaded into Protégé JPN, UiA 47

48 JPN, UiA 48

49 JPN, UiA 49

50 JPN, UiA 50

51 Even if no rule is specified the inference engine will still do some inferencing: JPN, UiA 51

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.: JPN, UiA 52

53 Task 1 Solution: (1) Every vegetarian dislikes all fish products. Vegetarian(?x) ^ FishProduct(?y) -> dislikes(?x,?y) JPN, UiA 53

54 Task 2: Anyone who ordered a dish that contains something he or she dislikes is unhappy. JPN, UiA 54

55 Task 2 solution: Anyone who ordered a dish that contains something he or she dislikes is unhappy. JPN, UiA 55

56 Task 3: Everything that can be ordered as a dish actually is a dish. Add the following to test: JPN, UiA 56

57 Task Solution 3: Everything that can be ordered as a dish actually is a dish. JPN, UiA 57

58 References Foundations of Semantic Web Technologies, Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph, Chapman & Hall/CRC, OGRlM/SWRL_Semantic_Web_Rule_Language_powerpoint_ppt_presentation Help SWRL Protégé 5: Jan Pettersen Nytun, UiA, page 58