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Properties and Individuals in OWL: Reasoning About Family History
Robert Stevens and Simon JuppBioHealth Informatics Group
University of [email protected]
k
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
Learning Objectives
• The separation in to TBox and ABox• The separation of classes and individuals• 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
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
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
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_bright_1965Types:Man
Individual: David_bright_1934Types:Person that hasSex some Male
• Class assertion on an individual• Indicates to which class an individual belongs
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
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 value richardIndividual Property Qualifier Successor
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_bright_1965 is a Person we know he has two parents, one mother and one father
Functional Characteristic
ObjectProperty: hasMotherDomain: PersonRange: WomanCharacteristics: FunctionalInverses: 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
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 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)
Inverse Functional Characteristic
• motherOf is not functional as one Woman can hold this property more than once
• The inverse hasMother is functional• The inverse of motherOf is functional: It is
inverse functionalmotherOf (invFunc)
margaret
richard
robert
motherOf (invFunc)
hasMother (func)
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
brotherOfRobert_David_bright_1965 Richard_bright_1941
brotherOf
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_bright_1965 Richard_bright_1962
siblingOf
Asymmetric Characteristic
• If x holds a property r with y• Then y cannot hold that property with x
hasFather
robert_David_bright_1965 David_bright_1934
HasFather
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_bright_1965 David_bright_1941
hasAncestor
William_george_bright
hasAncestor
hasAncestor
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
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 implies parentOf
• Don’t think about inheritance; think about implications and think of individuals
Inferences about Properties
• Run reasoner and see what we know about motherOf and hasMother
• Show domains and ranges inferred• See property hierarchy filled in
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 yearEven if we don’t know their valuesThe restrictions say what must be true of an individual
of that typeBy asserting the individual’s type to be Man, we know
these things to be trueThese facts are implied or entailedThere are many things that could be true of this
individual, but these things must be true
Some datatype properties
hasBirthYear
hasDeathYear• Domain of Person• Range of integer• Characteristic functional
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_bright_1965 David_bright_1934
hasAncestor
William_george_bright
hasAncestor
hasAncestor
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_bright_1934
Facts:
hasFather william_george_bright_1901
hasMother iris_ellen_archer_1907,
fatherOf robert_David_bright_1965,
fatherOf Richard_john_bright_1962
• What type does David_bright_1934 have?• How many children does he have?• Where in the hierarchy would be put
hasForeFather?
What is a Grandparent?
• We have parentage asserted• Can we infer grandparents?• A grandparent is a parent of my parent.• Don’t want transitivity on hasParent…• Otherwise my grandfather becomes my father
etc…• Want local transitivity
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_bright_1965 David_bright_1934
hasParent
William_george_bright
hasParent
hasGrandParent
Grandfathers
ObjectProperty: hasGrandfather
Domain: Person
Range: Man
SubPropertyChain: hasParent o hasFather
• hasParent followed by hasFather implies hasGrandfather
Robert_David_bright_1965 David_bright_1934
hasParent
William_george_bright
hasFather
hasGrandFather
Great Grandparents etc.
ObjectProperty: hasGreatGrandParent
SubPropertyChain: hasGrandParent o hasParent
• My grandparents parents are my great grandparents
Robert_David_bright_1965 William_george_bright_1901
hasGrandParent
Henry_edmond_bright
hasParent
hasGreatGrandParent
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?
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?
Using Individuals in Class Expressions
• The class of all Ancestor is easyHow about AncestorOfRobertStevens?
Class: AncestorOfRobertEquivalentTo: Personthat ancestorOf value robert_David_bright_1965
• robert_David_bright_1965 is a nominal• Instead of simply saying an individual from this class, we
specify the individual{robert_David_bright} is the class containing Robert David Stevens
• {robert, richard} is the class with richard and robert in it
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
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_bright_1965?• Just because we haven’t said he has children,
doesn’t mean he doesn’t have any?
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
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
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
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
Brothers and Siblings
• All inferred to be siblings of each other
david
peter
john
brotherOf
brotherOf
siblingOf
hasBrother
hasBrother
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
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
A Lesson on Cousins
• First cousins share a grandparent, but not a parentSecond 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
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…)
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
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
Simple and Complex Properties
• Properties can be either simple or complex• Some of our properties are complex• ancestorOf, uncleOf, parentOf…• Can’t do some things with complex properties
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
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
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
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
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
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
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 appropriate for this
domain• Good for teaching about individuals and
properties• More irregular and imcomplete things can be
hung off family history• Roles, processes…