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Properties and Individuals in OWL: Reasoning
About Family History
Robert Stevens and Simon Jupp
BioHealth Informatics Grou...
Introduction
• Pizza tutorial teaches the basics of OWL
• Using automated reasoning to build a sophisticated
T Box.
• Not ...
Learning Objectives
• The separation in to TBox and ABox
• The separation of classes and individuals and how to
make the d...
Why Family History?
• Family history rich with relationships
• Easy to have both a class and instance level
• Everyone has...
Families are People
Person Sex
Male
Female
What is a Person?
• A Person must have two parents
• A person necessarily has one mother and one
father
• A person necessa...
A Simple View on Sex
• This is a simple view on sex that will suffice
Person Sex
MaleFemaleMan Woman
hasSex
isA isA
Definitions of Man and Woman
Class: Man
EquivalentTo: Person
that hasSex some Male
• hasSex is Functional
Instances of Man and Woman
Individual: robert_david_stevens_1965
Types:
Man
Individual: david_stevens_1934
Types:
Person t...
TBox and ABox
• TBox – terminology box
• ABox – assertion box
• Historic terms
• TBox – classes (“schema”)
• ABox – indivi...
A Bit more Terminology
• Individual, instance, object
• Property, role
• Successor or filler of a property
• Qualifiers: S...
Demo 1
• Open Family-tree-0.owl
• Individuals: plain-individuals.owl
Asserting Parentage
• What do we know about each and every Person?
• Each and every Person has exactly two Parents
• Again...
Functional Characteristic
ObjectProperty: hasMother
Domain: Person
Range: Woman
Characteristics: Functional
Inverses: moth...
Description of Person
Class: Person
SubClassOf: DomainEntity
that hasMother some Woman
and hasFather some Man
Domain and Range
• Any individual holding the motherOf property can be
inferred to be of type Woman
• The domain constrain...
Inverse Functional Characteristic
• motherOf is not functional as one Woman can hold
this property more than once
• The in...
Demo 2
• Family-tree-1.owl
Irreflexive Characteristic
• An individual holding this property never holds it with
itself
• One is never ones own father...
Symmetric Characteristic
• The inverse of the property is the same
• If x is the sibling of y, then y is the sibling of x
...
Asymmetric Characteristic
• If x holds a property r with y
• Then y cannot hold that property with x
hasFather
Robert_davi...
Transitive Characteristic
• If x holds property r with y and y holds property r
with z then x holds property r with z
• Th...
Should I Say it Just Because it is True
• Not necessarily
• Ask what implications it drives
• Also ask if the characterist...
Property Hierarchies
• We can say that one property is the sub-property of
another property
motherOf SubPropertyOf parentO...
Inferences about Properties
• Run reasoner and see what we know about
motherOf and hasMother
• Show domains and ranges inf...
What do we Know of an Instance of Man?
• By giving an individual the type Man we know:
– He hasSex Male
– He has only one ...
Demo 3
• Family-tree-2.owl
Some datatype properties
hasBirthYear
hasDeathYear
• Domain of Person
• Range of integer
• Characteristic functional
Demo 4
• Infer which family members were Victorians
• Born between 1837-1901
Inferring One’s Ancestors
• My parents parents are my ancestors etc..
• Create a new super-property of hasParent, make it
...
Demo 5
• Family-tree-3.owl
• Add hasAncestor, look at property hierarchy
• What do we know about Robert?
David is Father of Robert
Individual: david_stevens_1934
Facts:
hasFather william_george_stevens_1901
hasMother iris_ellen...
Demo 6
• Family-tree-4.owl
• Assert robert parents
What is a Grandparent?
• We have parentage asserted
• Can we infer grandparents?
• A grandparent is a parent of my parent....
SubProperty Chains
ObjectPropety: hasGrandparent
Domain: Person
Range: Person
SubPropertyChain: hasParent o hasParent
• Th...
Grandfathers
ObjectProperty: hasGrandfather
Domain: Person
Range: Man
SubPropertyChain: hasParent o hasFather
• hasParent ...
Demo 7
• Family-tree-5.owl
• Create grandparent property chains
• What do we learn about Robert?
Great Grandparents etc.
ObjectProperty: hasGreatGrandParent
SubPropertyChain: hasGrandParent o hasParent
• My grandparents...
Superproperties of grandparent Properties
• Are hasGrandparent and hasGreatGrandparent etc.
subproperties of hasParent?
• ...
Hierarchies of Parentage Relationships
• Where do these parentage relationships go?
• All grandparents and great-grandpare...
Demo 8
• Great grand parents
Using Individuals in Class Expressions
• The class of all Ancestor is easy
How about AncestorOfRobertStevens?
Class: Ances...
Demo 9
• Family-tree-6.owl
OWL uses an open world assumption
• Just because something hasn’t been said doesn’t
mean it isn’t true
• hasMother is func...
The Open World and Individuals
• Ask for Woman that is motherOf min 3 Person
• What do we expect to happen?
• What does th...
What about my Uncle John?
• My Uncle John has four children
• Asking:
Man that fatherOf min 4 Person
doesn’t find my uncle...
Can infer that Individuals are Different
• If we have three individuals with different birth years
• And hasBirthYear is f...
Brothers
• Only done parentage so far
• David is brother of John
• John is brother of Peter
• Is brotherOf transitive?
• D...
Siblings
• brotherOf and sisterOf both sub-properties of
siblingOf
• siblingOf is symmetric and transitive
• Unlike brothe...
Brothers and Siblings
• All inferred to be siblings of each other
david
peter
john
brotherOf
brotherOf
siblingOf
hasBrothe...
Demo 10
• Familt-tree-6.owl
• Individuals-sibling.owl
• Siblings
• We can only infer that Peter and John are siblings
• br...
Aunts and Uncles
ObjectProperty: uncleOf
SubPropertyChain: brotherOf o fatherOf
• My parents siblings are my aunts and unc...
Demo 11
• Family-tree-7.owl
• Uncles and aunts
A Lesson on Cousins
• First cousins share a grandparent, but not a parent
Second cousins share a great grandparent, but no...
Characteristics of Cousin
• Symmetric: robert firstCousinOf James
• James firstCousinOf Robert
• Not transitive
• James’s ...
Sub-Property Chain for firstCousinOf
ObjectProperty: firstCousinOf
SubPropertyChain: hasParent o siblingOf o parentOf
• My...
Who are Robert’s First Cousins?
• Mart, Ian, Janet, william, Robert, richard, James, Clare, Julie,
Mark, Nicholas
• Robert...
Demo 13
• Define cousin and view entailments
Simple and Complex Properties
• Properties can be either simple or complex
• Some of our properties are complex
• ancestor...
Complex roles
• A property is complex when it forms a path
• Transitivity or sub-property chains form a path
David
brother...
Complex roles and Counting
• Counting i.e. cardinality; max 3, min 2, etc
• One cannot count with complex properties
• anc...
What one can do with SubProperty chains
• The pattern:
sub-property chain o property works  chain
hasGrandParent o hasPar...
Marriage
ObjectProperty: hasWife
SubPropertyChain: malePartnerIn o hasFemalePartner
• Want only one wife at a time
• Needs...
Demo 14
• Family-tree-8.owl
Extending aunt and uncle
• Now we have spouses we can do aunts and uncles
by marriage
• UncleOf implied by husbandOf o sis...
What Works
• Most things except cousins
• Full and half sibs don’t work
• Need some rules
• Also, using properties such as...
Should we Use OWL for this?
• Relational databases and/or Prolog do family history
much better than OWL
• Very regular and...
Acknowledgements
• Margaret Stevens
• Uli Sattler
• Dmitry Tsarkov
• Matthew Horridge
• Facilitated by the Ontogenesis net...
Reflexive Characteristic
• The reflexive property means an individual holding
this property always holds it with itself
• ...
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Properties and Individuals in OWL: Reasoning About Family History

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Slides used in an advanced OWL tutorial in 2012. The tutorial is based on family history and uses OWL individuals as a first class citizen in the learning.

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Properties and Individuals in OWL: Reasoning About Family History

  1. 1. Properties and Individuals in OWL: Reasoning About Family History Robert Stevens and Simon Jupp BioHealth Informatics Group University of Manchester Robert.Stevens@manchester.ac.uk
  2. 2. Introduction • Pizza tutorial teaches the basics of OWL • Using automated reasoning to build a sophisticated T Box. • Not much use of property hierarchies, domain and range constraints, property characteristics etc. • Especially not much use of individuals • This tutorial does all this along with some OWL2 features • An illustrated tutorial that you can follow
  3. 3. Learning Objectives • The separation in to TBox and ABox • The separation of classes and individuals and how to make the decision • Asserting facts about individuals • The effects of property hierarchies, property characteristics, domain/range constraints and role chains on inferences about individuals • The consequences of the open world assumption • The use of nominals • Some limits of OWL2
  4. 4. Why Family History? • Family history rich with relationships • Easy to have both a class and instance level • Everyone has a family, even if it is unknown • Assumption of a conventional western family structure
  5. 5. Families are People Person Sex Male Female
  6. 6. What is a Person? • A Person must have two parents • A person necessarily has one mother and one father • A person necessarily has one birth year • A person necessarily has ancestors • A person can have other relations • All these relationships are deterministic
  7. 7. A Simple View on Sex • This is a simple view on sex that will suffice Person Sex MaleFemaleMan Woman hasSex isA isA
  8. 8. Definitions of Man and Woman Class: Man EquivalentTo: Person that hasSex some Male • hasSex is Functional
  9. 9. Instances of Man and Woman Individual: robert_david_stevens_1965 Types: Man Individual: david_stevens_1934 Types: Person that hasSex some Male • Class assertion on an individual • Indicates to which class an individual belongs
  10. 10. TBox and ABox • TBox – terminology box • ABox – assertion box • Historic terms • TBox – classes (“schema”) • ABox – individuals (“data”) • Can have many, changing, ABoxes with one TBox
  11. 11. A Bit more Terminology • Individual, instance, object • Property, role • Successor or filler of a property • Qualifiers: SOME, ONLY, Cardinality • Class assertion and individual assertion robert hasBrother some richard Individual Property Qualifier Successor
  12. 12. Demo 1 • Open Family-tree-0.owl • Individuals: plain-individuals.owl
  13. 13. Asserting Parentage • What do we know about each and every Person? • Each and every Person has exactly two Parents • Again, we take a simple, biological view, of parentage for the moment • Simply by asserting that robert_david_stevens_1965 is a Person we know he has two parents, one mother and one father
  14. 14. Functional Characteristic ObjectProperty: hasMother Domain: Person Range: Woman Characteristics: Functional Inverses: motherOf • What do we know about the inverse? • motherOf has domain Woman • A Woman can be motherOf more than one Person • So inverse is not necessarily functional • The super-property, hasParent, is also not functional • A Person has more than one parent • Always think about individuals
  15. 15. Description of Person Class: Person SubClassOf: DomainEntity that hasMother some Woman and hasFather some Man
  16. 16. Domain and Range • Any individual holding the motherOf property can be inferred to be of type Woman • The domain constraint is a strong statement • The range constraint means only individuals of that type can be successors to the property; act as fillers • Both can drive inference • Domain and range can be inferred for the inverse (and are swapped)
  17. 17. Inverse Functional Characteristic • motherOf is not functional as one Woman can hold this property more than once • The inverse hasMother is function • The inverse of motherOf is functional: It is inverse functional motherOf (invFunc) margaret richard robert motherOf (invFunc) hasMother (func)
  18. 18. Demo 2 • Family-tree-1.owl
  19. 19. Irreflexive Characteristic • An individual holding this property never holds it with itself • One is never ones own father, but can be the father of others • By implication the inverse is also irreflexive brotherOf Robert_david_stevens_1965 Richard_stevens_1941 brotherOf
  20. 20. Symmetric Characteristic • The inverse of the property is the same • If x is the sibling of y, then y is the sibling of x • The property is its own inverse siblingOf Robert_david_stevens_1965 Richard_stevens_1941 siblingOf
  21. 21. Asymmetric Characteristic • If x holds a property r with y • Then y cannot hold that property with x hasFather Robert_david_stevens_1965 David_stevens_1941 HasFather
  22. 22. Transitive Characteristic • If x holds property r with y and y holds property r with z then x holds property r with z • The relationship is propagated along the chain • The inverse is also implied Robert_david_stevens_1965 David_stevens_1941 hasAncestor William_george_stevens hasAncestor hasAncestor
  23. 23. Should I Say it Just Because it is True • Not necessarily • Ask what implications it drives • Also ask if the characteristic is always the case • Sometimes it scuppers the reasoners
  24. 24. Property Hierarchies • We can say that one property is the sub-property of another property motherOf SubPropertyOf parentOf • A property can be the sub-property of more than one property • Can drive many inferences • An individual holding motherOf also holds parentOf • And so on until the root property
  25. 25. Inferences about Properties • Run reasoner and see what we know about motherOf and hasMother • Show domains and ranges inferred • See property hierarchy filled in
  26. 26. What do we Know of an Instance of Man? • By giving an individual the type Man we know: – He hasSex Male – He has only one mother, who is a Woman – Has only one father, who is a Man – He has a birth year Even if we don’t know their values The restrictions say what must be true of an individual of that type By asserting the individual’s type to be Man, we know these thing to be true These facts are implied or entailed There are many things that could be true of this individual, but these things must be true
  27. 27. Demo 3 • Family-tree-2.owl
  28. 28. Some datatype properties hasBirthYear hasDeathYear • Domain of Person • Range of integer • Characteristic functional
  29. 29. Demo 4 • Infer which family members were Victorians • Born between 1837-1901
  30. 30. Inferring One’s Ancestors • My parents parents are my ancestors etc.. • Create a new super-property of hasParent, make it transitive • Now, hasAncestor is implied by hasParent; it is entailed • hasAncestor forms a path Robert_david_stevens_1965 David_stevens_1941 hasAncestor William_george_stevens hasAncestor hasAncestor
  31. 31. Demo 5 • Family-tree-3.owl • Add hasAncestor, look at property hierarchy • What do we know about Robert?
  32. 32. David is Father of Robert Individual: david_stevens_1934 Facts: hasFather william_george_stevens_1901 hasMother iris_ellen_bowmaker_1907, fatherOf robert_david_stevens_1965, fatherOf richard_john_stevens_1962 • What type does david_stevens_1934 have? • How many children does he have? • Where in the hierarchy would be put hasForeFather?
  33. 33. Demo 6 • Family-tree-4.owl • Assert robert parents
  34. 34. What is a Grandparent? • We have parentage asserted • Can we infer grandparents? • A grandparent is a parent of my parent. • Don’t want transitivityon hasParent… • Otherwise my grandfather becomes my father etc… • Want local transitivity
  35. 35. SubProperty Chains ObjectPropety: hasGrandparent Domain: Person Range: Person SubPropertyChain: hasParent o hasParent • The chain hasParent followed by hasParent implies hasGrandparent • This forms a path • As usual, think of the individuals Robert_david_stevens_1965 David_stevens_1941 hasParent William_george_stevens hasParent hasGrandParent
  36. 36. Grandfathers ObjectProperty: hasGrandfather Domain: Person Range: Man SubPropertyChain: hasParent o hasFather • hasParent followed by hasFather implies hasGrandfather Robert_david_stevens_1965 David_stevens_1941 hasParent William_george_stevens hasFather hasGrandFather
  37. 37. Demo 7 • Family-tree-5.owl • Create grandparent property chains • What do we learn about Robert?
  38. 38. Great Grandparents etc. ObjectProperty: hasGreatGrandParent SubPropertyChain: hasGrandParent o hasParent • My grandparents parents are my great grandparents Robert_david_stevens_1965 William_geogre_stevens_1941 hasGrandParent Henry_edmond_stevens hasParent hasGreatGrandParent
  39. 39. Superproperties of grandparent Properties • Are hasGrandparent and hasGreatGrandparent etc. subproperties of hasParent? • Think about the implications at the level of individuals • Robert hasGrandParent william George • Robert hasGrandParent Iris Ellen • Does the fact that robert hasGrandfather William George imply he hasGrandparent William George? • Does this imply Robert hasParent William George? • All great grandparents are also grandparents • Is greatGrandParentOf a sub-property of grandParentOf?
  40. 40. Hierarchies of Parentage Relationships • Where do these parentage relationships go? • All grandparents and great-grandparents are also parents • All grandfathers are fathers • All great grandparents are grandparents • Should these parentage relationships like hasGrandparent be in a hierarchy underneath hasParent?
  41. 41. Demo 8 • Great grand parents
  42. 42. Using Individuals in Class Expressions • The class of all Ancestor is easy How about AncestorOfRobertStevens? Class: AncestorOfRobert EquivalentTo: Person that ancestorOf value robert_david_stevens_1965 • robert_david_stevens_1965 is a nominal • Instead of simply saying an individual from this class, we specify the individual {robert_david_stevens} is the class containing Robert David Stevens • {robert, richard} is the class with richard and robert in it
  43. 43. Demo 9 • Family-tree-6.owl
  44. 44. OWL uses an open world assumption • Just because something hasn’t been said doesn’t mean it isn’t true • hasMother is functional, so we know that property can only be held once • Do we know robert’s only brother is Richard? • We’ve said robert has a brother richard • We simply don’t know unless we limit the number of brothers • brotherOf only {richard} as a class assertion
  45. 45. The Open World and Individuals • Ask for Woman that is motherOf min 3 Person • What do we expect to happen? • What does the KB tell us about the children of robert_david_stevens_1965? • Just because we haven’t said he has children, doesn’t mean he doesn’t have any?
  46. 46. What about my Uncle John? • My Uncle John has four children • Asking: Man that fatherOf min 4 Person doesn’t find my uncle • Why not? • We haven’t told the KB that the four individuals asserted are actually different • In a Web environment, the same individual may be described at many locations with more than one URI • owl:differentFrom and owl:sameAs • Make all individuals different
  47. 47. Can infer that Individuals are Different • If we have three individuals with different birth years • And hasBirthYear is functional • Then we can infer those individuals are different without stating it directly
  48. 48. Brothers • Only done parentage so far • David is brother of John • John is brother of Peter • Is brotherOf transitive? • Domain of brotherOf is Man • What is the range? • William George is brotherOf Charlotte • So range must be person • William George brotherOf Charlotte • Charlote hasBrother William George
  49. 49. Siblings • brotherOf and sisterOf both sub-properties of siblingOf • siblingOf is symmetric and transitive • Unlike brother and sister, the inverse holds • William George is sibling of Charlotte • Charlotte is sibling of William George
  50. 50. Brothers and Siblings • All inferred to be siblings of each other david peter john brotherOf brotherOf siblingOf hasBrother hasBrother
  51. 51. Demo 10 • Familt-tree-6.owl • Individuals-sibling.owl • Siblings • We can only infer that Peter and John are siblings • brotherOf has domain Man and range Person • Even if we know Peter is a Man (he is fatherOf james) Man & siblingOf doesn’t imply brotherOf
  52. 52. Aunts and Uncles ObjectProperty: uncleOf SubPropertyChain: brotherOf o fatherOf • My parents siblings are my aunts and uncles • Cannot count with hasUncle David brotherOf Robert fatherOf uncleOf John
  53. 53. Demo 11 • Family-tree-7.owl • Uncles and aunts
  54. 54. A Lesson on Cousins • First cousins share a grandparent, but not a parent Second cousins share a great grandparent, but not a grandparent • Third cousins share a great great grandparent, but not a great grandparent • Degree gives closest common ancestor • Remove gives generation • My first cousins children are my first cousin once removed • Our common ancestor are my grandparents, but there is an added generation
  55. 55. Characteristics of Cousin • Symmetric: robert firstCousinOf James • James firstCousinOf Robert • Not transitive • James’s cousins are not my cousins (at least, not all of them…)
  56. 56. Sub-Property Chain for firstCousinOf ObjectProperty: firstCousinOf SubPropertyChain: hasParent o siblingOf o parentOf • My parents sibs are my aunts and uncles • Their children are my first cousins • Our common ancestor are my grandparents David hasParent Peter siblingOf firstCousinOf Robert James parentOf
  57. 57. Who are Robert’s First Cousins? • Mart, Ian, Janet, william, Robert, richard, James, Clare, Julie, Mark, Nicholas • Robert and Richard! • I’m my own cousin and so is my brother • My father is his own brother! • siblingOf is symmetric and transitive • David siblingOf John • John siblingOf David • There is path from David to David via John • So David is David’s brother • Making siblingOf irreflexive is a contradiction! • Inferences about cousins doesn’t work
  58. 58. Demo 13 • Define cousin and view entailments
  59. 59. Simple and Complex Properties • Properties can be either simple or complex • Some of our properties are complex • ancestorOf, uncleOf, parentOf… • Can’t do some thing with complex properties
  60. 60. Complex roles • A property is complex when it forms a path • Transitivity or sub-property chains form a path David brotherOf Robert fatherOf uncleOf John Robert David hasAncestor William hasAncestor hasAncestor Path
  61. 61. Complex roles and Counting • Counting i.e. cardinality; max 3, min 2, etc • One cannot count with complex properties • ancestorOf min 3 people doesn’t work • hasAncestor is complex; it forms a path • parentOf min 3 Person does work as parentOf is simple
  62. 62. What one can do with SubProperty chains • The pattern: sub-property chain o property works  chain hasGrandParent o hasParent  hasGreatGrandparent • will work hasParent o hasGrandParent  hasGreatGrandpaernt • will not
  63. 63. Marriage ObjectProperty: hasWife SubPropertyChain: malePartnerIn o hasFemalePartner • Want only one wife at a time • Needs some more sophisticated modelling of time – functionality will not do Marriage_m_and_d David Margaret hasMalePartnerIn hasFemalePartnerIn hasWife malePartnerIn femalePartnerIn
  64. 64. Demo 14 • Family-tree-8.owl
  65. 65. Extending aunt and uncle • Now we have spouses we can do aunts and uncles by marriage • UncleOf implied by husbandOf o sisterOf o parentOf • We can have more than one sub-property chain per property
  66. 66. What Works • Most things except cousins • Full and half sibs don’t work • Need some rules • Also, using properties such as grandparentOf and greatGrantParentOf in class expressions doesn’t always give the desired TBox • OWL2 features very powerful, but there are limitations
  67. 67. Should we Use OWL for this? • Relational databases and/or Prolog do family history much better than OWL • Very regular and complete knowledge • In some ways OWL not good for this domain • Good for teaching about inviduals and properties • More irregular and implete things can be hung off family history • Roles, processes…
  68. 68. Acknowledgements • Margaret Stevens • Uli Sattler • Dmitry Tsarkov • Matthew Horridge • Facilitated by the Ontogenesis network.
  69. 69. Reflexive Characteristic • The reflexive property means an individual holding this property always holds it with itself • One is always one of one’s own relations • By implication the inverse of hasRelation is also reflexive • Proper part of is not reflexive hasRelation Robert_david_stevens_1965 Margaret_stevens_1941 hasRelation

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