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Jarrar: ORM in Description Logic

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Lecture slides by Mustafa Jarrar at Birzeit University, Palestine. …

Lecture slides by Mustafa Jarrar at Birzeit University, Palestine.
See the course webpage at: http://jarrar-courses.blogspot.com/2011/09/knowledgeengineering-fall2011.html
and http://www.jarrar.info

and on Youtube:
http://www.youtube.com/watch?v=3_-HGnI6AZ0&list=PLDEA50C29F3D28257

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  • 1. Jarrar © 2011 1 ORM in Description Logic Lecture Notes on ORM in Description Logic Birzeit University 2011 Dr. Mustafa Jarrar University of Birzeit mjarrar@birzeit.edu www.jarrar.info Knowledge Engineering
  • 2. Jarrar © 2011 2 Outline • Part I: Introduction (Why Description logics) • Part II: Introduction to Description logics • Part III: Mapping ORM into Description logic • Something to think about 
  • 3. Jarrar © 2011 3 Reading • Mustafa Jarrar: Mapping ORM into the SHOIN/OWL Description Logic- Towards a Methodological and Expressive Graphical Notation for Ontology Engineering. In OTM workshops, proceeding of the International Workshop on Object-Role Modeling (ORM'07). Volume 4805, LNCS, Pages (729-741), Springer. ISBN: 9783540768890. Portogal. November, 2007. • D. Nardi, R. J. Brachman. An Introduction to Description Logics. In the Description Logic Handbook, edited by F. Baader, D. Calvanese, D.L. McGuinness, D. Nardi, P.F. Patel-Schneider, Cambridge University Press, 2002, pages 5-44. http://www.inf.unibz.it/~franconi/dl/course/dlhb/dlhb-01.pdf • Sean Bechhofer, “The DIG Description Logic Interface: DIG/1.1 ” http://racer-systems.com/dl.php?file=NativeLibraries%252FDIGinterface11.pdf&typ=file&name=DIGinterface11.pdf
  • 4. Jarrar © 2011 4 Remember: ORM has many Applications Database XML Schema Web (x)FormsBusiness Rules Ontology Originally Warehouse Later Requirements Engineering Record my recipes !
  • 5. Jarrar © 2011 5 An Information System Conceptual Schema Data Logical Schema DBMS Queryprocessor Apps Information System  Why do we need conceptual schemes? for designing Information systems at the conceptual level.  Each Information System is made for one organization.
  • 6. Jarrar © 2011 6 Conceptual Schema Data DBMS Logical Schema Queryprocessor Apps IS1 Conceptual Schema Data DBMS Logical Schema Queryprocessor Apps ISn New needs: Open data exchange, inter-organizational transactions, global queries… Agreed data schemes (XML, RDF) Ontologies/ Semantics (OWL) (Web) Information Systems
  • 7. Jarrar © 2011 7 Semantic Mediator (Web) Information Systems Bookstore Ontology
  • 8. Jarrar © 2011 8 Semantic Mediator (Web) Information Systems …. <owl:Class rdf:ID="Product" /> <owl:Class rdf:ID="Book"> <rdfs:subClassOf rdf:resource="#Product" /> </owl:Class> <owl:Class rdf:ID="Price" /> <owl:Class rdf:ID="Value" /> <owl:Class rdf:ID="Currency" /> <owl:Class rdf:ID="Title" /> <owl:Class rdf:ID="ISBN" /> <owl:Class rdf:ID="Author" /> <owl:ObjectProperty rdf:ID="Valuated-By"> <rdfs:domain rdf:resource="#Product" /> <rdfs:range rdf:resource="#Price" /> </owl:ObjectProperty> <owl:DataProperty rdf:ID=" Amounted-To .Value"> <rdfs:domain rdf:resource="#Price" /> <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/> </owl:ObjectProperty> <owl:DataProperty rdf:ID="Measured-In.Currency"> <rdfs:domain rdf:resource="#Price" /> <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/> … Bookstore Ontology Written in OWL
  • 9. Jarrar © 2011 9 OWL  The Web Ontology Language (W3C Standard)  Based on Description logic …. <owl:Class rdf:ID="Product" /> <owl:Class rdf:ID="Book"> <rdfs:subClassOf rdf:resource="#Product" /> </owl:Class> <owl:Class rdf:ID="Price" /> <owl:Class rdf:ID="Value" /> <owl:Class rdf:ID="Currency" /> <owl:Class rdf:ID="Title" /> <owl:Class rdf:ID="ISBN" /> <owl:Class rdf:ID="Author" /> <owl:ObjectProperty rdf:ID="Valuated-By"> <rdfs:domain rdf:resource="#Product" /> <rdfs:range rdf:resource="#Price" /> </owl:ObjectProperty> <owl:DataProperty rdf:ID=" Amounted-To .Value"> <rdfs:domain rdf:resource="#Price" /> <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/> </owl:ObjectProperty> …  Can we use ORM to Model OWL ontologies?
  • 10. Jarrar © 2011 10 First Order Logic (FOL) • FOL allows us to represent knowledge precisely (Syntax and Semantics). • However, representation alone is not enough. x PhDStudent(x)  Student (x) x Employee(x)  Person (x) x Student(x)  Person (x) x PhDStudent(x)  Employee (x) Person StudentEmployee PhD Student • We also need to process this knowledge and make use of it, i.e. Logical inference = (Reasoning).
  • 11. Jarrar © 2011 11 x PhDStudent(x)  Student (x) x Employee(x)  Person (x) x Student(x)  Person (x) x PhDStudent(x)  Employee (x) Person StudentEmployee PhD Student x PhDStudent(x)  Person (x) How to process the above axioms to know that an axiom can be derived from (=implied by) another axiom. First Order Logic (FOL) Reasoning:
  • 12. Jarrar © 2011 12 Person StudentEmployee PhD Student Find contradictions (satisfiability) x Student(x)  Employee (x) =  …etc. x PhDStudent(x)  Student (x) x Employee(x)  Person (x) x Student(x)  Person (x) x PhDStudent(x)  Employee (x) First Order Logic (FOL) Reasoning: How to process the above axioms to know that an axiom can be derived from (=implied by) another axiom.
  • 13. Jarrar © 2011 13 First Order Logic (FOL) Reasoning on FOL is far too complex (i.e. not decidable)  Here comes description logics.
  • 14. Jarrar © 2011 14 Introduction to Description Logics
  • 15. Jarrar © 2011 15 Description Logics • Description logics are a family of logics concerned with knowledge representation. • A description logic is a decidable fragment of first-order logic, associated with a set of automatic reasoning procedures. • The basic constructs for a description logic are the notion of a concept and the notion of a relationship. • Complex concept and relationship expressions can be constructed from atomic concepts and relationships with suitable constructs between them. • Example: Mother ⊑ Female ⊓ HasChild HumanMother ⊑ Female ⊓ HasChild.Person
  • 16. Jarrar © 2011 16 Description Logics Most known description logics are : A more practical and expressive description logic. C, D  A | ⊤ | ⊥|¬A | C ⊓ D | R.C | R.⊤ AL Very expressive description logic, Capable of representing most database constructs.DLRidf Very popular description logic. The logic underlying OWL. SROIQ The simplest and less expressive description logic. C, D  A | C ⊓ D | R.C | R FL¯
  • 17. Jarrar © 2011 17 Description logic AL • Example constructs:
  • 18. Jarrar © 2011 18 More AL Family Members • Disjunction (U) • Full existential quantification () • Number restrictions (N) • Full negation (C) • Example:
  • 19. Jarrar © 2011 19 DL as fragments of Predicate Logic
  • 20. Jarrar © 2011 20 DL Knowledge Base • DL Knowledge Base (KB) normally separated into 2 parts: – TBox is a set of axioms describing structure of domain (i.e., a conceptual schema), e.g.: • HappyFather  Man ⊓ hasChild.Female ⊓ … • Elephant ⊑ Animal ⊓ Large ⊓ Grey • transitive(ancestor) – ABox is a set of axioms describing a concrete situation (data), e.g.: • John:HappyFather • <John,Mary>:hasChild
  • 21. Jarrar © 2011 21 Terminologies or TBoxes
  • 22. Jarrar © 2011 22 Inference Services
  • 23. Jarrar © 2011 23 Inference services based on Satisfiability
  • 24. Jarrar © 2011 24 Inference service: concept subsumption Is a Mother always a Woman? Yes, Mother Subsumes Woman Description logic reasoners offer the computation of a Subsumption (taxonomy) of all named concepts
  • 25. Jarrar © 2011 25 • They offer reasoning services for multiple TBoxes and ABoxes. • They run as background reasoning engines. • They understand DIG, which is a simple protocol (based on HTTP) along with an XML Schema. Description Logic Reasoners <impliesc> <catom name=“Student"/> <catom name=“Person"/> </impliesc> Student ⊑ Person• Example: • For example:
  • 26. Jarrar © 2011 26 The SHOIN Description Logic • The logic underpinning OWL, the standard (W3C recommendation) Ontology Web Language. • A compromise between expressive power and computational complexity. • Does not support: n-ary relations, identification, functional dependencies.
  • 27. Jarrar © 2011 27 Mapping ORM to SHOIN
  • 28. Jarrar © 2011 28 …. <owl:Class rdf:ID="Product" /> <owl:Class rdf:ID="Book"> <rdfs:subClassOf rdf:resource="#Product" /> </owl:Class> <owl:Class rdf:ID="Price" /> <owl:Class rdf:ID="Value" /> <owl:Class rdf:ID="Currency" /> <owl:Class rdf:ID="Title" /> <owl:Class rdf:ID="ISBN" /> <owl:Class rdf:ID="Author" /> <owl:ObjectProperty rdf:ID="Valuated-By"> <rdfs:domain rdf:resource="#Product" /> <rdfs:range rdf:resource="#Price" /> </owl:ObjectProperty> <owl:DataProperty rdf:ID=" Amounted-To .Value"> <rdfs:domain rdf:resource="#Price" /> <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/> </owl:ObjectProperty> <owl:DataProperty rdf:ID="Measured-In.Currency"> <rdfs:domain rdf:resource="#Price" /> <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/> … (Web) Information Systems Semantic Mediator Bookstore Ontology
  • 29. Jarrar © 2011 29 Mapping ORM to Description Logic Why do we need this mapping for? • Use ORM as a graphical notation for Ontology/description logic languages. (The DL benefit from ORM) • Reasoning on ORM schemes automatically. (The ORM benefit from DL)
  • 30. Jarrar © 2011 30 Examples of reasoning services: - Satisfiability SAT(C,T ) iff there is a model I of T with CI   To know whether a concept can be populated or not (e.g. because of some axioms contradicting each other) - Subsumption SUBS(C, D,T ) iff CI ⊆ DI for all model I of T To know whether a concept is subsuming another concept (e.g. to find unwanted or missing subsumptions) - Redundancies EQUIV(C, D,T ) iff CI = DI for all model I of T To know whether two concepts are equal (e.g. to find out redundancies) Reasoning Services
  • 31. Jarrar © 2011 31 Reasoning on ORM Schemes  Schema satisfiability: A schema is satisfiable if and only if there is at least one concept in the schema that can be populated.  Concept satisfiability: A schema is satisfiable if and only if all concepts in the schema can be populated.  Role satisfiability: A schema is satisfiable if and only if all roles in the schema can be populated.  Concept satisfiability implies schema satiability.  Role satisfiability implies concept satiability.  Weak satisfiability  Strong satisfiability Person Course Teaches Studies {Math1, Prog1} 3-5
  • 32. Jarrar © 2011 32 Mapping ORM to DLR and SHOIN n-ary relations: -- No Support -- SHOIN
  • 33. Jarrar © 2011 33 Mapping ORM to DLR and SHOIN Binary relations: SHOIN
  • 34. Jarrar © 2011 34 Mapping ORM to DLR and SHOIN Unary roles: SHOIN
  • 35. Jarrar © 2011 35 Mapping ORM to DLR and SHOIN Role Mandatory: SHOIN
  • 36. Jarrar © 2011 36 Mapping ORM to DLR and SHOIN Disjunctive Mandatory: SHOIN
  • 37. Jarrar © 2011 37 Mapping ORM to DLR and SHOIN Role Uniqueness: SHOIN
  • 38. Jarrar © 2011 38 Mapping ORM to DLR and SHOIN Predicate Mandatory: -- No Support -- SHOIN
  • 39. Jarrar © 2011 39 Mapping ORM to DLR and SHOIN External Mandatory: -- No Support -- SHOIN
  • 40. Jarrar © 2011 40 Mapping ORM to DLR and SHOIN Role Frequency: SHOIN
  • 41. Jarrar © 2011 41 Mapping ORM to DLR and SHOIN Multiple-Role Frequency: -- No Support -- SHOIN
  • 42. Jarrar © 2011 42 Mapping ORM to DLR and SHOIN Subtypes: SHOIN
  • 43. Jarrar © 2011 43 Mapping ORM to DLR and SHOIN Total Subtypes: SHOIN
  • 44. Jarrar © 2011 44 Mapping ORM to DLR and SHOIN Exclusive Subtypes: SHOIN
  • 45. Jarrar © 2011 45 Mapping ORM to DLR and SHOIN Value Constraint: STRING: Number: SHOIN SHOIN
  • 46. Jarrar © 2011 46 Mapping ORM to DLR and SHOIN Role Subset Constraint: SHOIN
  • 47. Jarrar © 2011 47 Mapping ORM to DLR and SHOIN Predicate Subset Constraint: SHOIN
  • 48. Jarrar © 2011 48 Mapping ORM to DLR and SHOIN Role-sequence Subset Constraint: -- No Support -- SHOIN
  • 49. Jarrar © 2011 49 Mapping ORM to DLR and SHOIN Role Equality Constraint: SHOIN
  • 50. Jarrar © 2011 50 Mapping ORM to DLR and SHOIN Predicate Equality Constraint: SHOIN
  • 51. Jarrar © 2011 51 Mapping ORM to DLR and SHOIN Role-sequence Equality Constraint: -- No Support -- SHOIN
  • 52. Jarrar © 2011 52 Mapping ORM to DLR and SHOIN Role exclusion Constraint: SHOIN
  • 53. Jarrar © 2011 53 Mapping ORM to DLR and SHOIN Predicate Exclusion Constraint: SHOIN
  • 54. Jarrar © 2011 54 Mapping ORM to DLR and SHOIN Role- sequence Exclusion Constraint: -- No Support -- SHOIN
  • 55. Jarrar © 2011 55 Mapping ORM to DLR and SHOIN Objectification: SHOIN -- No Support --
  • 56. Jarrar © 2011 56 DogmaModeler  DogmaModeler is an ontology engineering tool  It uses ORM as a graphical notation  It uses Racer as a background reasoning engine Other functionalities of DogmaModeler:  Verbalization of ORM into 11 human languages.  Modularization of auto composition of ORM schemes  ….
  • 57. Jarrar © 2011 57 Home Work • Map your ORM model (project 3) into description logic. • Reason about your ORM model using Racer. • MS Word file containing: 1. You ORM model 2. Map ORM into DL 3. Map ORM into DIG and load it to Racer 4. Screen shorts of Racer results, that (a)your model is satisfiable, (b) your model is unsatisfiable (make something wrong) The next Lecture assumes that you know XML, if not please read about it.
  • 58. Jarrar © 2011 58 Conclusions and Discussion
  • 59. Jarrar © 2011 59 n-ary Relations Binary Relations Predicate Uniqueness Role Equality Predicate Equality Seq-Role Equality Irreflexive Role MandatorySybtype NUMBER Value Symmetric Unary Relations Disjunctive Mandatory Exclusive STRING Value Asymmetric Role Frequency Multi Role Frequency Total Objectification Anti Symmetric Role Uniqueness Role subset Predicate Subset Seq-Role Subset Intransitive External Uniqueness Role Exclusion Predicate Exclusion Seq-Role Exclusion Acyclic ORM Constructs and constraints MappedtoDLRMappedtoSHONOWLCannotmap
  • 60. Jarrar © 2011 60 Predicate Uniqueness Seq-Role Equality Seq-Role Subset Seq-Role Exclusion Acyclic Multi Role Frequency n-ary Relations Objectification External Uniqueness Binary Relations Role Equality Predicate Equality Irreflexive Role Mandatory NUMBER Value Symmetric Unary Relations Disjunctive Mandatory Exclusive STRING Value Asymmetric Total Anti Symmetric Role Uniqueness Role subset Predicate Subset Intransitive Role Exclusion Predicate Exclusion Role Frequency Sybtype Lesson 1: what is mapped to what
  • 61. Jarrar © 2011 61 Predicate Uniqueness Seq-Role Equality Seq-Role Subset Seq-Role Exclusion Acyclic Multi Role Frequency n-ary Relations Objectification External Uniqueness Binary Relations Role Equality Predicate Equality Irreflexive Role Mandatory NUMBER Value Symmetric Unary Relations Disjunctive Mandatory Exclusive STRING Value Asymmetric Total Anti Symmetric Role Uniqueness Role subset Predicate Subset Intransitive Role Exclusion Predicate Exclusion Role Frequency Sybtype Lesson 2: Decidable fragments Decidable
  • 62. Jarrar © 2011 62 Description Logic Reasoners a short tutorial on DIG
  • 63. Jarrar © 2011 63 • They offer reasoning services for multiple TBoxes and ABoxes. • They run as background reasoning engines. • They understand DIG, which is a simple protocol (based on HTTP) along with an XML Schema. Description Logic Reasoners <impliesc> <catom name="Student"/> <catom name="Person"/> </impliesc> Student ⊑ Person• Example: • For example:
  • 64. Jarrar © 2011 64 DIG Interface (http://dig.sourceforge.net/ ) S. Bechhofer: The DIG Description Logic Interface: DIG/1.1 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104.3837&rep=rep1&type=pdf
  • 65. Jarrar © 2011 65 DIG Interface (http://dig.sourceforge.net/ ) S. Bechhofer: The DIG Description Logic Interface: DIG/1.1 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104.3837&rep=rep1&type=pdf
  • 66. Jarrar © 2011 66 DIG Protocol • DIG is only an XML schema for a description logic along with ask/tell functionality • You write a new Knowledge base (using the DIG XML syntax), and send it to Racer using the TELL functionality. • You can then write you Query/Question (using the DIG, XML syntax), and send it to Racer using the ASK functionality. • You may communicate with the Racer through HTTP or SOAP.
  • 67. Jarrar © 2011 67 Create e a new Knowledge Base <?xml version="1.0" encoding="UTF-8"?> <newKB xmlns="http://dl.kr.org/dig/2003/02/lang" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://dl.kr.org/dig/2003/02/lang http://dl-web.man.ac.uk/dig/2003/02/dig.xsd"/> <?xml version="1.0" encoding="UTF-8"?> <response xmlns="http://dl.kr.org/dig/2003/02/lang" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://dl.kr.org/dig/2003/02/lang http://dl-web.man.ac.uk/dig/2003/02/dig.xsd"> <kb uri="urn:uuid:abcdefgh-1234-1234-12345689ab"/> The Response Message The newKB Message This URI should then be used during TELL and ASK requests made against the knowledge base
  • 68. Jarrar © 2011 68 Tell Syntax <?xml version="1.0" encoding="ISO-8859-1"?> <tells xmlns="http://dl.kr.org/dig/2003/02/lang" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://dl.kr.org/dig/2003/02/lang http://dl-web.man.ac.uk/dig/2003/02/dig.xsd" uri="urn:uuid:abcdefgh-1234-1234-12345689ab"> <defconcept name="driver"/> <equalc> <catom name="driver"/> <and> <catom name="person"/> <some> <ratom name="drives"/> <catom name="vehicle"/> </some> </and> </equalc> <defconcept name="person"/> <defconcept name="vehicle"/> <defrole name="drives"/> </tells> A TELL request must contain in its body a tells element, which itself consists of a number of tell statements. Example: Driver ⊑ Person ⊓ Drives.Vehicle
  • 69. Jarrar © 2011 69 Tell Syntax Tell Language Primitive Concept Introduction <defconcept name="CN"/> <defrole name="CN"/> <deffeature name="CN"/> <defattribute name="CN"/> <defindividual name="CN"/> Concept Axioms <impliesc>C1 C2</impliesc> <equalc>C1 C2</equalc> <disjoint>C1... Cn</disjoint> Role Axioms <impliesr>R1 R2</impliesc> <equalr>R1 R2</equalr> <domain>R E</domain> <range>R E</range> <rangeint>R</rangeint> <rangestring>R</rangestring> <transitive>R</transitive> <functional>R</functional> Individual Axioms <instanceof>I C</instanceof> <related>I1 R I2</related> <value>I A V</value> Concept Language Primitive Concepts <top/> <bottom/> <catom name="CN"/> Boolean Operators <and>E1... En</and> <or>E1... En</or> <not>E</not> Property Restrictions <some>R E</some> <all>R E</all> <atmost num="n">R E</atmost> <atleast num="n">R E</atleast> <iset>I1... In</iset> Concrete Domain Expressions <defined>A</defined> <stringmin val="s">A</stringmin> <stringmax val="s">A</stringmax> <stringequals val="s">A</stringequals> <stringrange min="s" max="t">A</stringrange> <intmin val="i">A</intmin> <intmax val="i">A</intmax> <intequals val="i">A</intequals> <intrange min="i" max="j">A</intrange> Role Expressions <ratom name="CN"/> <feature name="CN"/> <inverse>R</inverse> <attribute name="CN"/> <chain>F1... FN A</chain> Individuals <individual name="CN"/>
  • 70. Jarrar © 2011 70 Ask Syntax • An ASK request must contain in its body an asks element. • Multiple queries in one request is possible. <?xml version="1.0"?> <asks xmlns="http://dl.kr.org/dig/2003/02/lang"> xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://dl.kr.org/dig/2003/02/lang" http://dl-web.man.ac.uk/dig/2003/02/dig.xsd" uri="urn:uuid:abcdefgh-1234-1234-12345689ab"> <satisfiable id="q1"> <catom name="Vehicle"/> </satisfiable> <descendants id="q2"> <and> <catom name="person"/> <some> <ratom name="drives"/> <catom name="vehicle"/> </some> </and> </descendants> <types id="q3"> <individual name="JohnSmith"></individual> </types> </asks> KB |= Vehicle asks about satisfiability of the Vehicle concept asks for all those concepts subsumed by the description given, i.e. all the drivers a |  |= Peron(a) ⊓Drives.Vehicle asks for the known types of the given individual C |  |= C(JohnSmith)
  • 71. Jarrar © 2011 71 Ask Syntax Ask Language Primitive Concept Retrieval <allConceptNames/> <allRoleNames/> <allIndividuals/> Satisfiability <satisfiable>C</satisfiable> <subsumes>C1 C2</subsumes> <disjoint>C1 C2</disjoint> Concept Hierarchy <parents>C</parents> <children>C</children> <ancestors>C</ancestors> <descendants>C<descendants/> <equivalents>C</equivalents> Role Hierarchy <rparents>R</rparents> <rchildren>R</rchildren> <rancestors>R</rancestors> <rdescendants>R<rdescendants/> Individual Queries <instances>C</instances> <types>I</types> <instance>I C</instance> <roleFillers>I R</roleFillers> <relatedIndividuals>R</relatedIndividuals>