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Ontologies and Vocabularies


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Talk at SSSW2012, Cercedilla.

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Ontologies and Vocabularies

  1. 1. Ontologies and Vocabularies Sean Bechhofer School of Computer Science, University of Manchester, UK Ontology Languages, SSSW12
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  4. 4. Semantic Web • Metadata – Describe resources – No good unless everyone speaks the same language; • Terminologies – provide shared and common vocabularies of a domain, so search engines, agents, authors and users can communicate. – No good unless everyone means the same thing; • Ontologies – provide a shared and common understanding of a domain that can be communicated across people and applications, and will play a major role in supporting 4
  5. 5. Classes/Properties/Individuals • Many representation languages use an “object oriented model” with • Objects/Instances/Individuals – Elements of the domain of discourse • Types/Classes/Concepts – Sets of objects sharing certain characteristics • Relations/Properties/Roles – Sets of pairs (tuples) of objects • Such languages are/can be: – Well understood – Formally specified – (Relatively) easy to use – Amenable to machine processing 5
  6. 6. Structure of an Ontology Ontologies typically have two distinct components: • Names for important concepts in the domain – Elephant is a concept whose members are a kind of animal – Herbivore is a concept whose members are exactly those animals who eat only plants or parts of plants – AdultElephant is a concept whose members are exactly those elephants whose age is greater than 20 years • Background knowledge/constraints on the domain – An AdultElephant weighs at least 2,000 kg – All Elephants are either AfricanElephants or IndianElephants 6
  7. 7. Why Semantics? • What does an expression in an ontology mean? • The semantics of a language can tell us precisely how to interpret a complex expression. • Well defined semantics are vital if we are to support machine interpretability – They remove ambiguities in the interpretation of the descriptions. Telephone Black ? 7
  8. 8. What does RDF give us? • A mechanism for publishing data. • Single (simple) data model. • Syntactic consistency between names (IRIs). • Low level integration of data. – Mash the graphs together and we’re done. 8
  9. 9. RDF(S): RDF Schema • RDF gives a data model and serialisations, but it does not give any special meaning to schema vocabulary such as subClassOf or type – Interpretation is an arbitrary binary relation • RDF Schema extends RDF with a schema vocabulary that allows us to define basic vocabulary terms and the relations between those terms – Class, Property – type, subClassOf – range, domain 9
  10. 10. RDF(S) • These terms are the RDF Schema building blocks (constructors) used to create vocabularies: – <Person,type,Class> – <hasColleague,type,Property> – <Professor,subClassOf,Person> – <Carole,type,Professor> – <hasColleague,range,Person> – <hasColleague,domain,Person> • Semantics gives “extra meaning” to particular RDF predicates and resources – specifies how terms should be interpreted – allows us to draw inferences 10
  11. 11. RDF(S) Inference rdfs:Class rdf:type Person rdf:type rdfs:subClassOf rdf:type Academic rdfs:subClassOf rdf:subClassOf Lecturer 11
  12. 12. RDF(S) Inference rdfs:Class rdf:type Academic rdf:type rdfs:subClassOf Lecturer rdfs:type rdf:type Sean 12
  13. 13. RDF/RDF(S) “Liberality” • No distinction between classes and instances (individuals) <Species,type,Class> <Lion,type,Species> <Leo,type,Lion> • No distinction between language constructors and ontology vocabulary, so constructors can be applied to themselves/each other <type,range,Class> <Property,type,Class> <type,subPropertyOf,subClassOf> • In order to cope with this, RDF(S) has a particular non- standard model theory. 13
  14. 14. What does RDF(S) give us? • Ability to use simple schema/vocabularies when describing our resources. • Consistent vocabulary use and sharing. • Basic inference 14
  15. 15. Problems with RDF(S) • RDF(S) is too weak to describe resources in sufficient detail – No localised range and domain constraints  Can’t say that the range of hasChild is Person when applied to Persons and Elephant when applied to Elephants – No existence/cardinality constraints  Can’t say that all instances of Person have a mother that is also a Person, or that Persons have exactly 2 parents – No transitive, inverse or symmetrical properties  Can’t say that isPartOf is a transitive property, that hasPart is the inverse of isPartOf or that touches is symmetrical 15
  16. 16. OWL • OWL: Web Ontology Language • Extends existing Web standards – Such as XML, RDF, RDFS • Is (hopefully) easy to understand and use – Based on familiar KR idioms • Of “adequate” expressive power • Formally specified – Possible to provide automated reasoning support 16
  17. 17. The OWL Family Tree DAML RDF/RDF(S) DAML-ONT Joint EU/US Committee DAML+OIL OWL OWL2 Frames OIL W3C OntoKnowledge+Others Description Logics 17
  18. 18. Aside: Description Logics • A family of logic based Knowledge Representation formalisms – Descendants of semantic networks and KL-ONE – Describe domain in terms of concepts (classes), roles (relationships) and individuals • Distinguished by: – Formal semantics (typically model theoretic)  Decidable fragments of FOL  Closely related to Propositional Modal & Dynamic Logics – Provision of inference services  Sound and complete decision procedures for key problems  Implemented systems (highly optimised) 18
  19. 19. OWL (Direct) Semantics • Model theoretic semantics. An interpretation consists of – A domain of discourse (a collection of objects) – Functions mapping  classes to sets of objects  properties to sets of pairs of objects – Rules describe how to interpret the constructors and tell us when an interpretation is a model. • Semantics described in terms of – Individuals in a domain of discourse – (Binary) Properties that relate individuals – Classes or collections of individuals • A class description is a characterisation of the individuals that are members of that class. 19
  20. 20. OWL (Direct) Semantics • OWL has a number of operators for constructing class expressions. • These have an associated semantics which is given in terms of a domain: – Δ • And an interpretation function – I:concepts ! ℘(Δ) – I:properties ! ℘(Δ £ Δ) – I:individuals ! Δ • I is then extended to concept expressions. 20
  21. 21. OWL Class Constructors Constructor Example Interpretation Classes Class: Human I(Human) and (Human and Male) I(Human) Å I(Male) or (Doctor or Lawyer) I(Doctor) [ I(Lawyer) not not(Male) Δ I(Male) {} {john mary} {I(john), I(mary)} 21
  22. 22. OWL Class Constructors Constructor Example Interpretation some hasChild some Lawyer {x|9y.hx,yi2I(hasChild)^Æ y2I(Lawyer)} only hasChild only Doctor {x|8y.hx,yi2I(hasChild) ) y2I(Doctor)} min hasChild min 2 {x|#hx,yi2I(hasChild) ¸ 2} max hasChild max 2 {x|#hx,yi2I(hasChild) · 2} min hasChild min 2 Doctor {x|#{y|hx,yi2I(hasChild) ^Æ y2I (Doctor)} ¸ 2} max hasChild max 2 Lawyer {x|#{y|hx,yi2I(hasChild) ^Æ y2I (Lawyer)} · 2} 22
  23. 23. OWL Axioms • Axioms allow us to add further statements about arbitrary concept expressions and properties – Subclasses, Disjointness, Equivalence, characteristics of properties etc. • An interpretation I satisfies an axiom if the interpretation of the axiom is true. – Axioms constrain the allowed models – They provide the additional “assumptions” about the way in which the domain should be interpreted. • I satisfies or is a model of an ontology (or knowledge base) if the interpretation satisfies all the axioms in the knowledge base. 23
  24. 24. OWL Axioms Axiom Example Interpretation SubClassOf Class: Human I(Human) µ I(Animal) SubClassOf: Animal EquivalentTo Class: Man I(Man) = I(Human) Å I(Male) EquivalentTo: (Human and Male) Disjoint Disjoint: Animal, Plant I(Animal) Å I(Plant) = ; 24
  25. 25. OWL Individual Axioms Axiom Example Interpretation Individual Individual: Sean I(Sean) 2 I(Human) Types: Human Individual Individual: Sean hI(Sean),I(Oscar)i2I(worksWith) Facts: worksWith Oscar DifferentIndividuals Individual: Sean I(Sean) ≠ I(Oscar) DifferentFrom: Oscar SameIndividuals Individual: BarackObama I(BarackObama) = I SameAs: PresidentObama (PresidentObama) 25
  26. 26. OWL Property Axioms Axiom Example Interpretation SubPropertyOf ObjectProperty: hasMother I(hasMother) µ I(hasParent) SubpropertyOf: hasParent Domain ObjectProperty: owns 8x.hx,yi2I(owns) ) Domain: Person x2I(Person) Range ObjectProperty: employs 8x.hx,yi2I(employs) ) Range: Person y2I(Person) Transitive ObjectProperty: hasPart 8x,y,z. (hx,yi2I(hasPart) ^Æ hy,zi2I Characteristics: Transitive (hasPart)) ) hx,zi2I(hasPart) 26
  27. 27. Models • An OWL Ontology doesn’t define a single model, it is a set of constraints that define a set of possible models • No constraints (empty Ontology) means any model is possible • More constraints means fewer models • Too many constraints may mean no possible model (inconsistent Ontology) 27
  28. 28. Consequences • An ontology (collection of axioms) places constraints on the models that are allowed. • Consequences may be derived as a result of those constraints. • C subsumes D w.r.t. an ontology O iff for every model I of O, I(D) µ I(C) • C is equivalent to D w.r.t. an ontology O iff for every model I of O, I(C) = I(D) • C is satisfiable w.r.t. O iff there exists some model I of O s.t. I(C) ≠ ; • An ontology O is consistent iff there exists some model I of O. 28
  29. 29. Reasoning • A reasoner makes use of the information asserted in the ontology. • Based on the semantics described, a reasoner can help us to discover inferences that are a consequence of the knowledge that we’ve presented that we weren’t aware of beforehand. • Is this new knowledge? – What’s actually in the ontology? 29
  30. 30. Reasoning • Subsumption reasoning – Allows us to infer when one class is a subclass of another – B is a subclass of A if it is necessarily the case that (in all models), all instances of B must be instances of A. – This can be either due to an explicit assertion, or through some inference process based on an intensional definition. – Can then build concept hierarchies representing the taxonomy. – This is classification of classes. • Satisfiability reasoning – Tells us when a concept is unsatisfiable  i.e. when there is no model in which the interpretation of the 30 class is non-empty.
  31. 31. Instance Reasoning • Instance Retrieval  What are the instances of a particular class C?  Need not be a named class • Instantiation  What are the classes that x is an instance of? 31
  32. 32. Necessary and Sufficient Conditions • Classes can be described in terms of necessary and sufficient conditions. – This differs from some frame-based languages where we only have necessary conditions. • Necessary conditions – Must hold if an object is to be an instance of the class • Sufficient conditions – Those properties an object must have in order to be recognised as a member of the class. – Allows us to perform automated If it looks like a classification. duck and walks like a duck, then it’s a duck! 32
  33. 33. Misconceptions: Disjointness • By default, primitive classes are not disjoint. • Unless we explicitly say so, the description (Animal and Vegetable) is not unsatifiable. • Similarly with individuals. The so-called Unique Name Assumption (often present in DL languages) does not hold, and individuals are not considered to be distinct unless explicitly asserted to be so. 33
  34. 34. Misconceptions: Domain and Range • OWL allows us to specify the domain and range of properties. • Note that this is not interpreted as a constraint. • Rather, the domain and range assertions allow us to make inferences about individuals. • Consider the following: • ObjectProperty: employs Domain: Company Range: Person Individual: IBM Facts: employs Jim • If we haven’t said anything else about IBM or Jim, this is not an error. However, we can now infer that IBM is a Company and Jim is a Person. 34
  35. 35. Misconceptions: And/Or and Quantification • The logical connectives And and Or often cause confusion – Tea or Coffee? – Milk and Sugar? • Quantification can also be contrary to our intuition. – Universal quantification over an empty set is true. – Sean is a member of hasChild only Martian – Existential quantification may imply the existence of an individual that we don’t know the name of. 35
  36. 36. Misconceptions: Closed and Open Worlds • The standard semantics of OWL makes an Open World Assumption (OWA). – We cannot assume that all information is known about all the individuals in a domain. – Facilitates reasoning about the intensional definitions of classes. – Sometimes strange side effects • Closed World Assumption (CWA) – Named individuals are the only individuals in the domain • Negation as failure. – If we can’t deduce that x is an A, then we know it must be 36
  37. 37. Annotations • OWL defines annotation properties. • These allow us to assert information about things (classes, properties, individuals) that don’t contribute to the logical knowledge. – No semantics (in the direct semantics) • Information not about the domain but about the modelling or description of the domain – e.g. DC style creation metadata • Annotations could also be used to support applications – e.g. labels (cf SKOS.....) 37
  38. 38. Profiles • OWL Profiles describe subsets of the language that offer the potential for simpler/more efficient implementation • OWL EL – Roughly existential quantification of variables. • OWL QL – No class expressions in existential quantifications. – Query answering via rewrites into standard relational queries • OWL RL – Amenable to implementation using rule-based technologies. 38
  39. 39. Lightweight Vocabularies • For many applications, lightweight representations are more appropriate. • Thesauri, classification schemes, taxonomies and other controlled vocabularies – Many of these already exist and are in use in cultural heritage, library sciences, medicine etc. – Often have some taxonomic structure, but with a less precise semantics. 39
  40. 40. Concept Schemes • A concept scheme is a set of concepts, potentially including statements about relationships between those concepts – Broader Terms – Narrower Terms – Related Terms – Synonyms, usage information etc. • Concept schemes aren’t formal ontologies in the way that OWL ontologies are formal ontologies – Concepts are not intended to me interpreted as sets of things in the same way 40
  41. 41. SKOS: Simple Knowledge Organisation • SKOS provides an RDF vocabulary for the representation of such schemes. • Designed with a focus on Retrieval Scenarios A. Single controlled vocabulary used to index and then retrieve objects B. Different controlled vocabularies used to index and retrieve objects • Mappings then required between the vocabularies – Initial use cases/requirements focus on these tasks • Not worrying about activities like Natural Language translation 41
  42. 42. Knowledge Organisation SystemsThesaurus: Controlled vocabulary in which concepts are represented bypreferred terms, formally organised so that paradigmatic relationshipsbetween the concepts are made explicit, and the preferred terms areaccompanied by lead-in entries for synonyms or quasi-synonyms. Thesaurus Related Terms Taxonomy Hierarchy Authority File Preferred Terms Synonym Ring Equivalent Terms Controlled Vocabulary Collection of Terms Controlled vocabularies: designed for use in classifying or indexing documents and for searching them.
  43. 43. Concepts vs Terms • SKOS adopts a concept-based (as opposed to term-based) approach • Concepts associated with lexical labels • Relationships expressed between concepts. • Possibility of expressing relationships between terms through SKOS-XL.
  44. 44. SKOS Exampleanimals NT catscats UF domestic cats RT wildcats BT animals SN used only for domestic catsdomestic cats USE catswildcats Graphic: Antoine Isaac
  45. 45. SKOS Model
  46. 46. Labelling • Lexical Labels associated with Concepts – Preferred: one per language – Alternate: variants, – Hidden: mis-spellings • No domains stated, so usage possible on any resource. • Labels pairwise disjoint. • Label Extension (SKOS-XL) provides additional support for descriptions of labels and links between them – E.g. acronyms, abbreviations
  47. 47. Documentation • A number of documentation properties • Not intended to be comprehensive • Extension points
  48. 48. Semantic Relations • Hierarchical and Associative • Broader/Narrower • Loose (i.e. no) semantics – A publishing vehicle, not a set of thesaurus construction guidelines • Domain/Range restrictions on semantic relations • broader/narrower not transitive in SKOS
  49. 49. Mapping Relations • Subproperties of Semantic Relations • Intended for cross-scheme usage – Although no formal enforcement
  50. 50. SKOS and OWL • SKOS itself is defined as an OWL ontology. • A particular SKOS vocabulary is an instantiation of that ontology/schema – SKOS Concept is a Class, particular concepts are instances of that class • Allows use of OWL mechanisms to define properties of SKOS (e.g. the querying of the transitive closure of broader). –
  51. 51. Transitivity of Semantic Relations • Broader/narrower not transitive in SKOS – Addition of broaderTransitive • Separate assertions from inferences • Thus can still query across transitive closure of broader. – User confusion with transitivity and inheritance.
  52. 52. SKOS and OWL • SKOS and OWL are intended for different purposes. – OWL allows the explicit modelling/description of a domain  Support for inference, automated classificationm detection of inconsistencies etc. – SKOS provides vocabulary and navigational structure • Interactions between representations – Presenting OWL ontologies as SKOS vocabularies – Enriching SKOS vocabularies as OWL ontologies. – Use of SKOS as annotation vocabulary
  53. 53. Hands On • Explore some example vocabularies in order to understand the semantics. • Investigate what the inferences are that we can draw, based on the class definitions and additional axioms in the ontologies. 53