Departamento de Inform

1

• Universidade do Minho
• Departamento de Informática
• Lic. Matemática e Ciências de Computação
• Laboratório de Métodos Formais
• Marlene Azevedo
• marlene.azevedo_at_correio.ci.uminho.pt

2

• Integration of OntoClean in XOL
• XOL

3
The Objectives

• Motivations
• Ontology
• XOL Language
• OntoClean Method
• XOL
• Example
• Future Work

4
Motivations

• Know How acquired
• Stimulant subject
• Topic Maps specification

5
Ontology

• an ontology is, simply, a specification of a
  conceptualization
• 
  
  by Gruber
• An ontology is a description (like a formal
  specification of a program) of the concepts and
  relationships that can exist for an agent or a
  community of agents
• Ontologies are about languages for expressing
  contracts between entities
• Ontologies provide a way of capturing a shared
  understanding of terms that can be used by humans
  and programs to aid in information exchange and
  gives a method of providing a specification of a
  controlled vocabulary.

6
XOL LanguageIntroduction

• The language, called XOL, is designed to provide
  a format for exchanging ontology definitions
  among a set of interested parties
• The syntax of XOL is based on XML
• The design of XOL deliberately uses a generic
  approach to define ontologies, meaning that the
  single set of XML tags (defined by a single XML
  DTD) defined for XOL can describe any and every
  ontology.
• Significant differences between an ontology
• and an DTD.

Invariants
7
XOL LanguageComparing DTD and Ontologies

• There is nothing in a DTD that corresponds to
  the is-a relationship of classes that is usually
  central in an ontology
• DTDs lack any notion of inheritance
• DTDs provide a rather poor means for defining the
  semantics of elementary tags
• DTDs define the order in which tags appear in a
  document.

8
XOL Language

• ltontologygt
• ltnamegt...lt/namegt
• ltkb-typegt...lt/kb-typegt
• ltpackagegt...lt/packagegt
• ltversiongt...lt/versiongt
• ltdocumentationgt...lt/documentationgt
• ltclassgt...lt/classgt
• ltclassgt...lt/classgt
• ...
• ltslotgt...lt/slotgt
• ltslotgt...lt/slotgt
• ...
• ltindividualgt...lt/individualgt
• ltindividualgt...lt/individualgt
• ...
• lt/ontologygt

9
XOL LanguageTypes Specification

• lt!ELEMENT (module ontology kb database
  dataset) (name, ( kb-type db-type)?, package?,
  version?, documentation?, class, slot,
  individual)gt
• module, ontology, kb, database, dataset are all
  synonymous
• Ontology N Name
• C1 Kb-type Db-type
• P Package
• V Version
• D Documentation
• C Classes
• S Slots
• I Individuals
• inv ont snameCC(ont) and snameSS(ont) and
  snameII(ont) and snameCS(ont) and
  snameCI(ont) and snameSI(ont) and
  subClass(ont) and transClass(ont)

10
XOL Language

• ltclassgt
• ltnamegt...lt/namegt
• ltdocumentationgt...lt/documentationgt
• ltsubclass-ofgt...lt/subclass-ofgt
• lt/classgt

11
XOL LanguageTypes Specification

• lt!ELEMENT class ( (name, documentation?,
• ( subclass-of
  instance-of slot-values))gt
• Classes C-Id Class
• C-Id token
• Class N Name
• D Documentation
• C2 (C-Id Slot-values)-set
• P C-Id-set

12
XOL Language

• ltslotgt
• ltnamegt...lt/namegt
• ltdocumentationgt...lt/documentationgt
• ltdomaingt...lt/domaingt
• ltslot-value-typegt...lt/slot-value-typegt
• lt/slotgt

13
XOL LanguageTypes Specification

• lt!ELEMENT slot (name, documentation?, ( domain
  slot-value-type slot-inverse slot-cardinality
  slot-maximum-cardinality slot-minimum-cardinali
  ty slot-numeric-minimum slot-numeric-maximum
  slot-collection-type slot-values ) gt
• Slots S-Id Slot
• S-Id token
• Slot N Name
• D Documentation
• C3 Slot-Ch-set
• A SlotAtt
• P C-Id-set

14
XOL LanguageTypes Specification

• lt!ATTLIST slot
• type ( template own )
  "own"gt
• SlotAtt T (Template OWN)
• Template token

15
XOL Language

• ltindividualgt
• ltnamegt...lt/namegt
• ltdocumentationgt...lt/documentationgt
• ltinstance-ofgt...lt/instance-ofgt
• ltslot-valuesgt
• ltnamegt...lt/namegt
• ltvaluegt...lt/valuegt
• lt/slot-valuesgt
• lt/individualgt

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XOL LanguageTypes Specification

• lt!ELEMENT individual
• (name, documentation?,
  (type slot-values)gt
• Individuals I -Id Individual
• I -Id token
• Individual N Name
• D Documentation
• C4 (Type Slot-values)-set
• P C-Id-set

17
XOL LanguageTypes Specification

• lt!ELEMENT slot-values (name, value,
  (facet-values value-type inverse cardinality
  maximum-cardinality minimum-cardinality
  numeric-minimum numeric-maximum some-values
  collection-type documentation-in-frame))gt
• Slot-values N Name
• V Value-set
• C5 Val_Ch-set

lt!ELEMENT facet-values (name, value)gt Facet-valu
es N Name V
Value-set
18
XOL LanguageInvariants Specification

• Function snameCC
• Specification
• snameCC Ontology -gt bool
• snameCC(ont) forall c1 in set dom ont.C
• (forall c2 in set (dom ont.C)\c1
  ont.C(c1).N ltgt ont.C(c2).N)
• Description
• The same name may not be used for two classes

19
XOL LanguageInvariants Specification

• Function snameSS
• Specification
• snameSS Ontology -gt bool
• snameSS(ont) forall s1 in set dom ont.S
• (forall s2 in set (dom ont.S)\s1
  ont.S(s1).N ltgt ont.S(s2).N)
• Description
• The same name may not be used for two slots

20
XOL LanguageInvariants Specification

• Function snameII
• Specification
• snameII Ontology -gt bool
• snameII(ont) forall i1 in set dom ont.I
• (forall i2 in set (dom ont.I)\i1
  ont.I(i1).N ltgt ont.I(i2).N)
• Description
• The same name may not be used for two
  individuals

21
XOL LanguageInvariants Specification

• Function snameCS
• Specification
• snameCS Ontology -gt bool
• snameCS(ont) forall s in set rng ont.S
  (forall c1 in set dom ont.C
  ont.C(c1).N ltgt s.N)
• Description
• The same name may not be used for class and a
  slot

22
XOL LanguageInvariants Specification

• Function snameCI
• Specification
• snameCI Ontology -gt bool
• snameCI(ont) forall i in set rng ont.I
  (forall c1 in set dom ont.C
  ont.C(c1).N ltgt i.N)
• Description
• The same name may not be used for class and an
  individual

23
XOL LanguageInvariants Specification

• Function snameSI
• Specification
• snameSI Ontology -gt bool
• snameSI(ont) forall i in set rng ont.I
  (forall s1 in set dom ont.S
  ont.s(s1).N ltgt i.N)
• Description
• The same name may not be used for a slot and
  an individual

24
XOL LanguageInvariants Specification

• Function subClass
• Specification
• subClass Ontology -gt bool
• subClass(ont) (forall c in set rng ont.C
• (forall tid in set c.C2
  is_Class(ont.C(tid)) gt tid in set dom
  ont.C and is_Slot(ont.S(tid)) gt tid in set dom
  ont.S and
• 
  is_Individual(ont.I(tid)) gt tid in set dom
  ont.I) and
• c.P ltgt nil
  gt c.P subset dom ont.C) and
• (forall s in set rng ont.S s.P
  ltgt nil gt s.P subset dom ont.C)
  and
• (forall i in set rng ont.I i.P
  ltgt nil gt i.P subset dom ont.C)
• Description
• Each class must be defined earlier than a
  subclass

25
XOL LanguageInvariants Specification

• Function transClass
• Specification
• transClass Ontology -gt bool
• transClass(ont) forall c in set (rng ont.C
  union rng ont.S union
• rng ont.I)
  dinter getParentsC(ont.C, c) and
• 
  dinter getParentsS(ont.C, c) and
• 
  dinter getParentsI(ont.C, c) )
• Description
• If class A is a subclass of class B, which
  in turn is a subclass of class C, only the
  subclass-of link between A and B should be
  included in the XOL file.
• The getParents function is defined for each
  kind of possible element in an Ontology, i.e.,
  Class, Slot and Individual. This way, it
  calculates a set of set of parents of the current
  node, using the relative level of each parent to
  decide in witch set to put him. The result is a
  structure describing each different level of
  parents the node has.

26
OntoClean MethodMeta-Properties

• It is a method to clean taxonomies according to
  notions such as rigidity, identity, unity and
  dependence. The definition of that notions refer
  to properties of properties and that are called
  meta-properties.
• Meta-Properties R Rigidity
• I Identity
• U Unity
• D Dependence

27
OntoClean MethodRigidity

• A property P is
• Rigid (R), if and only if is necessarily
  essential to all instances
• Non-rigid (-R), if and only if is not essential
  to some of its instances
• Anti-rigid (R), if and only if is not essential
  to all its instances.
• Rigidity RIGID NON RIGID ANTI
  RIGID

28
OntoClean MethodIdentity

• A property P
• Carries an IC (I or -I otherwise), if and only
  if all its instances can be (re)identified by
  means of suitable sameness relation
• Supplies an IC (O or -O otherwise), if and only
  if such criterion is not inherited by any
  subsuming property.
• Identity CARRIES_IC NOTCARRIES_IC
• SUPPLIES_IC NOTSUPPLIES_IC

29
OntoClean MethodUnity

• A property P
• Carries unity (U or -U otherwise), if there is a
  common unifying relation R such that all the
  instances of P are wholes under R
• Carries anti-unity (U), if all its instances can
  possible be non-wholes (U implies -U).
• Unity CARRIES_UC NOTCARRIES_UC
• ANTI-UNITY

30
OntoClean MethodDependence

• A property P is
• Constantly dependent (D or -D otherwise), if and
  only if, for all its instances, there exists
  something they are constantly dependent on.
• Dependence DEPENDENT NON_DEPENDENT

31
OntoClean Method Constraints and Assumptions

• R must subsume R, i.e., R cant subsume R
• U must subsume U, i.e., -U cant subsume U
• U must subsume U, i.e., U cant subsume U
• I must subsume I, i.e., -I cant subsume I
• D must subsume D, i.e., -D cant subsume D
• Properties with incomplete ICs/UCs are disjoint.

32
OntoClean Method All possible combinations of
the meta-properties
33
XOLArchitecture
OntoClean
XOL
Specification
XOL
34
XOLTypes Specification

• Class alteration
• Classes C-Id Class
• C-Id token
• Class N Name
• D Documentation
• C2 (C-Id Slot-values)-set
• P C-Id-set
• M Meta-Properties

35
XOLInvariants Specification

• Addiction meta-properties invariants
• Function antiRig
• Specification
• antiRig Ontology -gt bool
• antiRig(ont) forall c in set rng ont.C
• (c.M).R ltAnti_Rigidgt gt
  forall cid in set c.C2
• cid in set dom ont.C gt
  (ont.C(cid).M).R ltgt ltRigidgt
• Description
• An Anti-Rigid class cannot have a Rigid
  subclass

36
XOLInvariants Specification

• Function unity
• Specification
• unity Ontology -gt bool
• unity(ont) forall c in set rng ont.C
• (c.M).U ltCarries_UCgt gt forall cid in
  set c.C2
• cid in set dom ont.C gt (ont.C(cid).M).U
  ltgt ltNotCarries_UCgt
• Description
• A Carries-UC class cannot have a NotCarries_UC
  subclass

37
XOLInvariants Specification

• Function antiUnity
• Specification
• antiUnity Ontology -gt bool
• antiUnity(ont) forall c in set rng ont.C
• (c.M).U ltAnti_Unitygt gt forall cid in
  set c.C2
• cid in set dom ont.C gt (ont.C(cid).M).U
  ltgt ltCarries_UCgt
• Description
• An Anti-Unity class cannot have a Carries_UC
  subclass

38
XOLInvariants Specification

• Function ident
• Specification
• ident Ontology -gt bool
• ident(ont) forall c in set rng ont.C
• (c.M).I ltCarries_ICgt gt forall cid
  in set c.C2
• cid in set dom ont.C gt
  (ont.C(cid).M).I ltgt ltNotCarries_ICgt
• Description
• An Carries_IC class cannot have a NotCarries_IC
  subclass

39
XOLInvariants Specification

• Function depend
• Specification
• depend Ontology -gt bool
• depend(ont) forall c in set rng ont.C
• (c.M).D ltDependentgt gt forall cid in set
  c.C2
• cid in set dom ont.C gt (ont.C(cid).M).D
  ltgt ltNon_Dependentgt
• Description
• An Dependent class cannot have a Non_Dependent
  subclass

40
XOL

• Consider some basic design principles
• be clear about the domain
• take identity seriously
• isolate a basic taxonomic structure make an
  explicit distinction between types and roles (
  and other property kinds)
• WELL-FOUNDED ONTOLOGY.

41
XOLExample

• ontology OntologyOntology mk_OntologyOntology
  (
• "Genealogy",
• "ocelot",
• "user",
• "",
• "",
• 1 -gt mk_OntologyClass (
• "Person",
• "The class of all
  persons",
• 2,3,
• nil,
• mk_OntologyMeta_Properti
  es(ltRigidgt,ltNotCarries_ICgt,
• 
  ltCarries_UCgt,ltNon_Depende
  ntgt)),
• 1 -gt mk_OntologySlot(
• "year-of-birth",
• "An integer that
  represents the year the person was born",
• "person","1","1800","int
  eger",
• mk_OntologySlotAtt(ltowngt
  ),
• 1 ),

42
XOL

• The main contributions that my work has
  accomplished are
• to provide a stronger ontological commitments in
  order to get a disciplined taxonomy
• to reduce the risk of classification mistakes in
  the ontology development process
• to simplify the update and maintenance process.

43
Future Work

• Adding OntoClean top-level to XOL
• XOL2VDM
• VDM2XOL
• Graphic Interface.