Knowledge Representation Part VII Protg RDFS OWL Jan

Knowledge Representation Part VII Protégé / RDFS / OWL / ++ Jan Pettersen Nytun, Ui. A 1

S O P • • Outline Protégé example RDFS OWL Some W 3 C documents concerning OWL 2 Jan Pettersen Nytun, Ui. A, Ontologies, page 2

S P O The Semantic Web Language Stack Hierarchy of languages, where each layer exploits and uses capabilities of the layers below. / XML Schema Jan Pettersen Nytun, Ui. A, page 3

S P O Individuals [4] Jan Pettersen Nytun, Ui. A, page 4

S P O Setting Default Namespace Explicitly • I found some problems like double #’s in the stored file when not explicitly stating the namespace. Explicitly stating the default namespace Jan Pettersen Nytun, Ui. A, page 5

S P O Turle File @prefix : <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#>. @prefix owl: <http: //www. w 3. org/2002/07/owl#>. @prefix rdf: <http: //www. w 3. org/1999/02/22 -rdf-syntax-ns#>. @prefix xml: <http: //www. w 3. org/XML/1998/namespace>. @prefix xsd: <http: //www. w 3. org/2001/XMLSchema#>. @prefix rdfs: <http: //www. w 3. org/2000/01/rdf-schema#>. @base <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#> rdf: type owl: Ontology. Jan Pettersen Nytun, Ui. A, page 6

S P O Turle File Continues. . . ############################ # # Object Properties # ############################ : has. Sibling rdf: type owl: Object. Property. : lives. In rdf: type owl: Object. Property. Jan Pettersen Nytun, Ui. A, page 7

S P O Turle File Continues. . . ################################# # # Individuals # ################################# : England rdf: type owl: Named. Individual , owl: Thing. : Gemma rdf: type owl: Named. Individual , owl: Thing. : Matthew rdf: type owl: Named. Individual , owl: Thing ; : lives. In : England ; : has. Sibling : Gemma. Jan Pettersen Nytun, Ui. A, page 8

S P O Adding Classes Jan Pettersen Nytun, Ui. A, page 9

S P O ############################# # # Classes # ############################# : Country rdf: type owl: Class. : Person rdf: type owl: Class. Jan Pettersen Nytun, Ui. A, page 10

S P O # Individuals : England rdf: type : Country , owl: Named. Individual. : Gemma rdf: type : Person , owl: Named. Individual. : Matthew rdf: type : Person , owl: Named. Individual ; : lives. In : England ; : has. Sibling : Gemma. Jan Pettersen Nytun, Ui. A, page 11

S P O [4]: In OWL classes are built up of descriptions that specify the conditions that must be satisfied by an individual for it to be a member of the class. Jan Pettersen Nytun, Ui. A, page 12

S P O Which Syntax Does Protégé Uses? Jan Pettersen Nytun, Ui. A, Ontologies, page 13

S P O Protégé Uses The Manchester OWL Syntax in Dialog Windows • The Manchester syntax [OWL 2 Manchester Syntax] is an OWL syntax that is designed to be easier for non-logicians to read. Jan Pettersen Nytun, Ui. A, Ontologies, page 14

S P O Save Ontology Using The Manchester Syntax Prefix: : <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#> Prefix: owl: <http: //www. w 3. org/2002/07/owl#> Prefix: rdf: <http: //www. w 3. org/1999/02/22 -rdf-syntax-ns#> Prefix: xml: <http: //www. w 3. org/XML/1998/namespace> Prefix: xsd: <http: //www. w 3. org/2001/XMLSchema#> Prefix: rdfs: <http: //www. w 3. org/2000/01/rdf-schema#> Ontology: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#> Object. Property: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#lives. In> Object. Property: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#has. Sibling> Class: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Person> Class: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Country> Jan Pettersen Nytun, Ui. A, Ontologies, page 15

Individual: Matthew Types: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Person> Facts: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#lives. In> <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#England>, <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#has. Sibling> <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Gemma> Individual: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Gemma> Types: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Person> Individual: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#England> Types: <http: //www. uia. no/IKT 437/janpettersennytun/ontologies/lecture 5#Country>

S O P • • Outline Protégé example RDFS OWL Some W 3 C documents concerning OWL 2 Jan Pettersen Nytun, Ui. A, Ontologies, page 17

S P O RDFS Allows definition of (simple) ontologies. RDFS gives some fundamental concepts, e. g. : • sub. Class. Of • sub. Property. Of • Domain and range • … Jan Pettersen Nytun, Ui. A, 18

S P O rdfs: sub. Class. Of The members of one class (the subclass) are also members of the other (the super class). : Female rdf: type owl: Class ; rdfs: sub. Class. Of : Human. Tools like reasoners “understands” the semantics of sub. Class. Of. Jan Pettersen Nytun, Ui. A, 19

S P O rdfs: sub. Property. Of The pair related by one property (the sub property) are included in the other (the super property). : has. Son rdf: type owl: Object. Property ; rdfs: sub. Property. Of : is. Parent. To. Jan Pettersen Nytun, Ui. A, 20

S P O Property Domains and Ranges • Properties link individuals from the domain to individuals from the range (or to “data” if for instance type is String). • Pizza ontology example: - the property has. Topping links individuals belonging to class Pizza (domain) to individuals belonging to the class of Pizza. Topping (range). • It is important to realize that in OWL domains and ranges should not be viewed as only constraints to be checked. They are used as `axioms' in reasoning. Jan Pettersen Nytun, Ui. A, 21

S P O Domain and Range can be used to describe a property. They determine the class membership of individuals related by the property. Given the 2 triples: : employer rdfs: domain : Person : employer rdfs: range : Organization From Wikipedia, the free encyclopedia Then triple: : John : employer : Company. X Requires that: - : John is necessarily a : Person - : Company. X is necessarily a : Organization Jan Pettersen Nytun, Ui. A, 22

S P O Multiple Classes As The Range For A Property This is interpreted as the intersection of the classes. For example, if the range of a property has the classes Man and Woman, the range of the property is interpreted as Man intersection Woman (this range would then be very small in number of individuals since not many are man and woman at the same time). Jan Pettersen Nytun, Ui. A , 23

S P O Did not work for me! Jan Pettersen Nytun, Ui. A, page 24

S P O This Seems to Work Fine! some. Pizza and some. Topping are individuals stated to be of type Thing Jan Pettersen Nytun, Ui. A, page 25

S P O Limitations Of RDFS [5] …modelers often need even richer and more expressive primitives to specify the formal semantics of Web resources… For example, one cannot state in RDFS that “this class is equivalent to this other class”, and cannot specify cardinality constraints. Jan Pettersen Nytun, Ui. A, 26

S O P • • Outline Protégé example RDFS OWL Some W 3 C documents concerning OWL 2 Jan Pettersen Nytun, Ui. A, Ontologies, page 27

S P O OWL extends the possibilities found in RDFS, e. g. : • equivalent. Class • inverse. Of • transitive. Property • Symetric. Property • … Jan Pettersen Nytun, Ui. A, 28

S P O Part Of OWL Metamodel [5] Jan Pettersen Nytun, Ui. A, Ontologies, page 29

S P O Unique Name Assumption (UNA) in Logic • UNA different names always refer to different entities in the world. • Protégé-OWL is based on UNA. • OWL is not based on UNA. OWL supplies explicit constructs: – owl: same. As (property) two given names or identifiers (e. g. , URIs) refer to the same individual or entity. – owl: different. From (property) two given names or identifiers (e. g. , URIs) refer to different individuals or entities. Jan Pettersen Nytun, Ui. A, page 30

S P O Disjoint Classes • OWL Classes are assumed to “overlap”, e. g. , an individual may be of several classes. • It is however possible to specify that two classes are disjoint. Knowledge Representation Part III, JPN, Ui. A Jan Pettersen Nytun, Ui. A , 31

S P OWL Property types O • There are two main types of properties: – Object properties. – Datatype properties. • Additionally: Annotation properties can be used to add metadata (data about data). Knowledge Representation Part II, JPN, Ui. A 32

S P O Property Characteristics OWL allows the meaning of properties to be enriched through the use of property characteristics. E. g. , inverse property. Knowledge Representation Part III, JPN, Ui. A 33

S P O Inverse Property • If some property links individual A to individual B then its inverse property will link individual B to individual A. • For example, Figure 4. 16 shows the property has. Parent and its inverse property has. Child. If Matthew has. Parent Jean, then because of the inverse property we can infer that Jean has. Child Matthew. Knowledge Representation Part III, JPN, Ui. A 34

S P O Functional Properties • A functional property connects only one object or literal to a subject. E. g. , it is only possible to have one birth mother Knowledge Representation Part III, JPN, Ui. A 35

S P O Functional Properties Continues … Mapping functional property to UML: It is possible to define an association as functional by specifying the upper multiplicity of the navigable end as being 0. . 1 Person Female is. Birth. Mother. To * 0. . 1 has. Birth. Mother Knowledge Representation Part III, JPN, Ui. A 36

S P O Inverse Functional Properties • If a property is inverse functional then it means that the inverse property is functional. Knowledge Representation Part III, JPN, Ui. A 37

S P O Functional / Inverse Functional Properties Inverse functional properties are similar, but in the reverse direction. Person Female is. Birth. Mother. To * Inverse Functional Property 0. . 1 has. Birth. Mother JPN, Ui. A 38

S P O Functional / Inverse Functional Properties continues … • Both object properties and datatype properties can be declared as "functional“ but not “functional inverse”. • [http: //stackoverflow. com/questions/21487939/what-is-the-difference-betweendatatypeproperty-objectproperty-functionalpro]: we cannot have the equivalence between the conditions that p is an inverse functional property and that p-1 is a functional property because datatype properties cannot have inverses. RDF does not allow literal values as the subjects of triples. 39

S P O More Property Characteristics If a property is transitive, and the property relates individual a to individual b, and also individual b to individual c, then we can infer that individual a is related to individual c via property P. E. g. , sub. Region. Of JPN, Ui. A 40

S P O More Property Characteristics If a property P is symmetric, and the property relates individual a to individual b then individual b is also related to individual a via property P. E. g. , has. Sibling JPN, Ui. A 41

S P O More Property Characteristics If a property P is asymmetric, and the property relates individual a to individual b then individual b cannot be related to individual a via property P. E. g. , is. Mother. To JPN, Ui. A 42

S P O More Property Characteristics A property P is said to be reflexive when the property must relate individual to itself. E. g. , has. Relative (everybody has himself as a relative). This does not necessarily mean that every two individuals which are related by a reflexive property are identical. JPN, Ui. A 43

S parent. Of P O More Property Characteristics Irreflexive, meaning that no individual can be related to itself by such a role. E. g. , has. Parent Knowledge Representation Part III, JPN, Ui. A 44

S P O OWL Restrictions • Three main categories: – Quantifier Restrictions • existential restrictions • universal restrictions – Cardinality Restrictions – has. Value Restrictions Jan Pettersen Nytun, Ui. A, Ontologies, page 45

S P O New version of Protégé calls it “Subclass of”

S P O Existential Restrictions A restriction containing an owl: some. Values. From constraint describes a class of all individuals for which at least one value of the property concerned is an instance of the class description or a data value in the data range. Jan Pettersen Nytun, Ui. A, Ontologies, page 47

S P O Cardinality in dialog window should be ignored (it is 1. . *) Jan Pettersen Nytun, Ui. A, Ontologies, page 48

S P O In Turtle Representation pizza: Pizza rdf: type owl: Class ; rdfs: label "Pizza"@en ; At least one pizza base! rdfs: sub. Class. Of [ rdf: type owl: Restriction ; owl: on. Property pizza: has. Base ; owl: some. Values. From pizza: Pizza. Base ] ; … Jan Pettersen Nytun, Ui. A, page 49

S P O Jan Pettersen Nytun, Ui. A, Ontologies, page 50

pizza: Margherita rdf: type owl: Class ; Only = owl: all. Values. From rdfs: label "Margherita"@pt ; rdfs: sub. Class. Of pizza: Named. Pizza , [ rdf: type owl: Restriction ; owl: on. Property pizza: has. Topping ; owl: all. Values. From [ rdf: type owl: Class ; owl: union. Of ( pizza: Mozzarella. Topping pizza: Tomato. Topping ) ] , …

S P O Jan Pettersen Nytun, Ui. A, Ontologies, page 52

S P O There is no “+” for adding; conditions comes from superclass! Jan Pettersen Nytun, Ui. A, Ontologies, page 53

S P O Multiple Inheritance from Anonymous Classes : Pizza rdf: type owl: Class ; rdfs: sub. Class. Of [ rdf: type owl: Restriction ; owl: on. Property : has. Topping ; owl: some. Values. From : Pizza. Topping ] , [ rdf: type owl: Restriction ; owl: on. Property : has. Base ; owl: some. Values. From : Pizza. Base ]. Jan Pettersen Nytun, Ui. A, Ontologies, page 54

S P O Reasoner Finding Inconsistency The actual reason that Probe. Inconsistent. Topping has been detected to be inconsistent is because its superclasses Vegetable. Topping and Cheese. Topping are disjoint from each other. Jan Pettersen Nytun, Ui. A, Ontologies, page 55

S P O Difference Between sub. Class. Of and equivalent. Class # Red wine is a subclass of all things that have a red color. : Red. Wine a owl: Class ; rdfs: sub. Class. Of Necessary [ a owl: Restriction ; owl: on. Property : color ; owl: has. Value red^^<http: //www. w 3. org/2001/XMLSchema#string> ]. # The set of red things is exactly the same as the class of things that have the value # "red" for its color property. : Red. Thing a owl: Class ; owl: equivalent. Class Sufficient [ a owl: Restriction ; owl: on. Property : color ; owl: has. Value red^^<http: //www. w 3. org/2001/XMLSchema#string> ] Jan Pettersen Nytun, Ui. A, Ontologies, page 56

S P O Using Necessary AND Sufficient Conditions Jan Pettersen Nytun, Ui. A, Ontologies, page 57

S P O Jan Pettersen Nytun, Ui. A, Ontologies, page 58

S O P • • Outline Protégé example RDFS OWL Some W 3 C documents concerning OWL 2 Jan Pettersen Nytun, Ui. A, Ontologies, page 59

S P O OWL Some Documents From W 3 C Where to start: OWL 2 Web Ontology Language Document Overview (Second Edition) (http: //www. w 3. org/TR/2012/REC-owl 2 -overview-20121211/) 60

OWL 2 Syntaxes [http: //www. semantic-web-book. org/w/images/7/75/W 2011 -08 -OWL-Syntax. pdf]:

Syntaxes [OWL 2 Web Ontology Language Document Overview ]: Name of Syntax Specification Status Purpose RDF/XML Mapping to RDF Graphs, RDF/XML Mandatory Interchange (can be written and read by all conformant OWL 2 software) OWL/XML Serialization Optional Easier to process using XML tools Functional Syntax Structural Specification Optional Easier to see the formal structure of ontologies Manchester Syntax Optional Easier to read/write DL Ontologies Turtle Mapping to RDF Graphs, Turtle Optional, Not from OWL-WG Easier to read/write RDF triples 62

S P O Any OWL 2 ontology can also be viewed as an RDF graph. . . The OWL 2 Quick Reference Guide [http: //www. w 3. org/TR/2012/REC-owl 2 -quick-reference-20121211/] provides a simple overview of these two views of OWL 2, laid out side by side. 63

S P O The OWL 2 Quick Reference Guide - Example 8. 2. 2 Universal Quantification A universal class expression Object. All. Values. From( OPE CE ) consists of an object property expression OPE and a class expression CE, and it contains all those individuals that are connected by OPE only to individuals that are instances of CE. Provided that OPE is simple according to the definition in Section 11, such a class expression can be seen as a syntactic shortcut for the class expression Object. Max. Cardinality( 0 OPE Object. Complement. Of( CE ) ). Object. All. Values. From : = 'Object. All. Values. From' '(' Object. Property. Expression Class. Expression ')' 64

The OWL 2 Quick Reference Guide – Example Continues… Example: Consider the ontology consisting of the following axioms. Object. Property. Assertion( a: has. Pet a: Peter a: Brian ) Brian is a pet of Peter. Class. Assertion( a: Dog a: Brian ) Brian is a dog. Class. Assertion( Object. Max. Cardinality( 1 a: has. Pet ) a: Peter ) Peter has at most one pet. Language Feature Functional Syntax RDF Syntax class assertion Class. Assertion(C a) a rdf: type C. positive object property assertion Object. Property. Assertion( PN a 1 a 2 ) a 1 PN a 2. maximum cardinality Object. Max. Cardinality(n P) _: x rdf: type owl: Restriction. _: x owl: on. Property P. _: x owl: max. Cardinality n.

Semantics [OWL 2 Web Ontology Language Document Overview ]: The OWL 2 Structural Specification document defines the abstract structure of OWL 2 ontologies, but it does not define their meaning. The Direct Semantics [OWL 2 Direct Semantics] and the RDF-Based Semantics [OWL 2 RDF-Based Semantics] provide two alternative ways of assigning meaning to OWL 2 ontologies, with a correspondence theorem providing a link between the two. These two semantics are used by reasoners and other tools, e. g. , to answer class consistency, subsumption and instance retrieval queries. 66

Semantics [OWL 2 Web Ontology Language Document Overview ]: The Direct Semantics assigns meaning directly to ontology structures, resulting in a semantics compatible with the model theoretic semantics of the SROIQ description logic—a fragment of first order logic with useful computational properties. The advantage of this close connection is that the extensive description logic literature and implementation experience can be directly exploited by OWL 2 tools. . Ontologies that satisfy these syntactic conditions are called OWL 2 DL ontologies. 67

OWL 2 Web Ontology Language Direct Semantics (http: //www. w 3. org/TR/owl 2 -direct-semantics/): This document provides the direct model-theoretic semantics for OWL 2, which is compatible with the description logic SROIQ. Furthermore, this document defines the most common inference problems for OWL 2. (Paper about SROIQ: The Even More Irresistible SROIQ. Ian. Horrocks and Oliver. Kutz and Ulrike. Sattler , The University of Manchester , http: //www. cs. man. ac. uk/~sattler/publications/KR-06 -SROIQ. pdf ) 68

Sematic Description – Example [OWL 2 Web Ontology Language Direct Semantics ]: Object. Max. Cardinality( n OPE ) { x | #{ y | ( x , y ) ∈ (OPE)OP } ≤ n } (For S a set, #S denotes the number of elements in S. ) 69

The Manchester OWL Syntax [http: //webont. org/owled/2006/accepted. Long/submission_9. pdf] : 70

The Manchester OWL Syntax Continues… [http: //webont. org/owled/2006/accepted. Long/submission_9. pdf] : 71

S P O References [1] Book: David Poole and Alan Mackworth, Artificial Intelligence: Foundations of Computational Agents, Cambridge University Press, 2010, http: //artint. info/ [2] http: //www. w 3. org/TR/swbp-n-ary. Relations/ [3] RDF 1. 1 Primer, W 3 C Working Group Note, 24 June 2014 [4] A Practical Guide To Building OWL Ontologies Using Protégé 4 and CO-ODE Tools Edition 1. 3, Matthew Horridge [5] http: //www. w 3. org/TR/2009/REC-owl 2 -syntax-20091027/ Jan Pettersen Nytun, Ui. A, Propositional Calculus, page 72