Properties and Individuals in OWL Reasoning About Family

Properties and Individuals in OWL: Reasoning About Family History Robert Stevens and Simon Jupp Bio. Health Informatics Group University of Manchester First. Name. Last. Name@manchester. ac. uk

Resources • Protégé 4 build 113 • Ontologies: http: //cs. man. ac. uk/~sjupp/family

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 OWL 2 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 OWL 2

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

Families are People Male Person Sex Female

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 is. A Man Sex is. A Woman Female has. Sex Male

Definitions of Man and Woman Class: Man Equivalent. To: Person that has. Sex some Male • has. Sex is Functional

Instances of Man and Woman Individual: robert_David_bright_1965 Types: Man Individual: David_bright_1934 Types: Person that has. Sex 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 has. Brother value richard Individual Property Qualifier Successor

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, 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 Object. Property: has. Mother Domain: Person Range: Woman Characteristics: Functional Inverses: mother. Of • • What do we know about the inverse? mother. Of has domain Woman A Woman can be mother. Of more than one Person So inverse is not necessarily functional The super-property, has. Parent, is also not functional A Person has more than one parent Always think about individuals

Description of Person Class: Person Sub. Class. Of: Domain. Entity that has. Mother some Woman and has. Father some Man

Domain and Range • Any individual holding the mother. Of 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 • mother. Of is not functional as one Woman can hold this property more than once • The inverse has. Mother is functional • The inverse of mother. Of is functional: It is inverse functional mother. Of (inv. Func) robert margaret has. Mother (func) richard mother. Of (inv. Func)

Demo 2 • Family-tree-1. owl

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 brother. Of Robert_David_bright_1965 Richard_bright_1941 • By implication the inverse is also irreflexive

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 Robert_David_bright_1965 Richard_bright_1962 sibling. Of

Asymmetric Characteristic • If x holds a property r with y • Then y cannot hold that property with x robert_David_bright_1965 David_bright_1934 Has. Father has. Father

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 has. Ancestor David_bright_1941 William_george_bright has. Ancestor

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 mother. Of Sub. Property. Of parent. Of • A property can be the sub-property of more than one property • Can drive many inferences • An individual holding mother. Of also implies parent. Of • Don’t think about inheritance; think about implications and think of individuals

Inferences about Properties • Run reasoner and see what we know about mother. Of and has. Mother • 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 has. Sex 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 things 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

Demo 3 • Family-tree-2. owl

Some datatype properties has. Birth. Year has. Death. Year • 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 are my ancestors etc. . • Create a new super-property of has. Parent, make it transitive • Now, has. Ancestor is implied by has. Parent; it is entailed • has. Ancestor forms a path Robert_David_bright_1965 has. Ancestor David_bright_1934 William_george_bright has. Ancestor

Demo 5 • Family-tree-3. owl • Add has. Ancestor, look at property hierarchy • What do we know about Robert?

David is Father of Robert Individual: David_bright_1934 Facts: has. Father william_george_bright_1901 has. Mother iris_ellen_archer_1907, father. Of robert_David_bright_1965, father. Of Richard_john_bright_1962 • What type does David_bright_1934 have? • How many children does he have? • Where in the hierarchy would be put has. Fore. Father?

Demo 6 • Family-tree-4. owl • Assert robert’s parents

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 has. Parent… Otherwise my grandfather becomes my father etc… Want local transitivity

Sub. Property Chains Object. Propety: has. Grandparent Domain: Person Range: Person Sub. Property. Chain: has. Parent o has. Parent • The chain has. Parent followed by has. Parent implies has. Grandparent • This forms a path • As usual, think of the individuals Robert_David_bright_1965 has. Parent David_bright_1934 William_george_bright has. Parent has. Grand. Parent

Grandfathers Object. Property: has. Grandfather Domain: Person Range: Man Sub. Property. Chain: has. Parent o has. Father • has. Parent followed by has. Father implies has. Grandfather Robert_David_bright_1965 has. Parent David_bright_1934 William_george_bright has. Father has. Grand. Father

Demo 7 • Family-tree-5. owl • Create grandparent property chains • What do we learn about Robert?

Great Grandparents etc. Object. Property: has. Great. Grand. Parent Sub. Property. Chain: has. Grand. Parent o has. Parent • My grandparents are my great grandparents Robert_David_bright_1965 William_george_bright_1901 has. Grand. Parent has. Great. Grand. Parent Henry_edmond_bright

Superproperties of grandparent Properties • Are has. Grandparent and has. Great. Grandparent etc. subproperties of has. Parent? • Think about the implications at the level of individuals • Robert has. Grand. Parent william George • Robert has. Grand. Parent Iris Ellen • Does the fact that robert has. Grandfather William George imply he has. Grandparent William George? • Does this imply Robert has. Parent William George? • All great grandparents are also grandparents • Is great. Grand. Parent. Of a sub-property of grand. Parent. Of?

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 has. Grandparent be in a hierarchy underneath has. Parent?

Demo 8 • Great grand parents

Using Individuals in Class Expressions • The class of all Ancestor is easy How about Ancestor. Of. Robert. Stevens? Class: Ancestor. Of. Robert Equivalent. To: Person that ancestor. Of 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

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 • has. Mother 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 • brother. Of only {richard} as a class assertion

The Open World and Individuals • Ask for Woman that is mother. Of 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 father. Of 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: different. From and owl: same. As Make all individuals different

Can infer that Individuals are Different • If we have three individuals with different birth years • And has. Birth. Year 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 is brother of Peter Is brother. Of transitive? Domain of brother. Of is Man What is the range? William George is brother. Of Charlotte So range must be person William George brother. Of Charlotte Charlote has. Brother William George

Siblings • brother. Of and sister. Of both sub-properties of sibling. Of • sibling. Of 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 has. Brother peter david brother. Of sibling. Of brother. Of john has. Brother • All inferred to be siblings of each other

Demo 10 • • • Familt-tree-6. owl Individuals-sibling. owl Siblings We can only infer that Peter and John are siblings brother. Of has domain Man and range Person Even if we know Peter is a Man (he is father. Of james) Man & sibling. Of doesn’t imply brother. Of

Aunts and Uncles Object. Property: uncle. Of Sub. Property. Chain: brother. Of o father. Of • My parents siblings are my aunts and uncles • Cannot count with has. Uncle Robert David John father. Of brother. Of uncle. Of

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 not a grandparent • Third cousins share a 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 first. Cousin. Of James first. Cousin. Of Robert Not transitive James’s cousins are not my cousins (at least, not all of them…)

Sub-Property Chain for first. Cousin. Of Object. Property: first. Cousin. Of Sub. Property. Chain: has. Parent o sibling. Of o parent. Of • My parents sibs are my aunts and uncles • Their children are my first cousins • Our common ancestor are my grandparents has. Parent James Peter David Robert sibling. Of first. Cousin. Of parent. Of

Demo 13 • Define cousin and view entailments

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! • sibling. Of is symmetric and transitive • David sibling. Of John • John sibling. Of David • There is path from David to David via John • So David is David’s brother • Making sibling. Of 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 ancestor. Of, uncle. Of, parent. Of… 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 Robert David John father. Of brother. Of uncle. Of Path Robert David William has. Ancestor

Complex roles and Counting • • • Counting i. e. cardinality; max 3, min 2, etc One cannot count with complex properties ancestor. Of min 3 people doesn’t work has. Ancestor is complex; it forms a path parent. Of min 3 Person does work as parent. Of is simple

What one can do with Sub. Property chains • The pattern: sub-property chain o property works chain has. Grand. Parent o has. Parent has. Great. Grandparent • will work has. Parent o has. Grand. Parent has. Great. Grandpaernt • will not

Marriage Object. Property: has. Wife Sub. Property. Chain: male. Partner. In o has. Female. Partner. In David has. Male. Partner. In Marriage_m_and_d has. Wife has. Female. Partner. In Margaret female. Partner. In • Want only one wife at a time • Needs some more sophisticated modelling of time – functionality will not do

Demo 14 • Family-tree-8. owl

Extending aunt and uncle • Now we have spouses we can do aunts and uncles by marriage • Uncle. Of implied by husband. Of o sister. Of o parent. Of • We can have more than one sub-property chain per property

Demo 15 • Add an extra sub-property chain to aunt. Of and uncle. Of

What Works • • Most things except cousins Full and half sibs don’t work Need some rules Also, using properties such as grandparent. Of and great. Grant. Parent. Of in class expressions doesn’t always give the desired TBox • OWL 2 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…

Acknowledgements • • Margaret Stevens Uli Sattler Dmitry Tsarkov Matthew Horridge • Facilitated by the Ontogenesis network.