Composition, Parts and Wholes COMP60421 Sean Bechhofer University - PowerPoint PPT Presentation

Composition, Parts and Wholes COMP60421 Sean Bechhofer University of Manchester sean.bechhofer@manchester.ac.uk 1

Composition or Aggregation • Forming an object whole using other objects as parts • Treating complex things as a single object • What are the primary composition relationships? • What inferences can we make? • What might we have in our representation languages to support this? http://www.flickr.com/photos/hartini/2429653007/ 2

Parts & wholes: Some examples • Bristles are part of a toothbrush • Wheels are part of a shopping trolley • A car is partly iron • A cappuccino is partly milk • A meter is part of a kilometer • Manchester is part of England • A tree is part of a forest • A slice of pie is part of the pie http://www.flickr.com/photos/aramisfirefly/4585596077 • A book chapter is part of a book • Stan Laurel is part of Laurel and Hardy • These are different kinds of composition, with different characteristics and properties. • Confusing them may result in incorrect (or undesirable) inferences. 3

Properties of Composition • Winston et. al. describe properties of composition • Configuration/Functionality – Do the parts bear a functional or structural relationship to one another or the object they constitute? – functional/non-functional • Homeomerous – Are the parts the same kind of thing as the whole? – homeomerous/non-homeomerous • Invariance – Can the parts be separated from the whole? – separable/inseparable • We can then discuss combinations of these properties. – We’ll consider Odell’s classification 4

functional Component-Integral Object non-homeomeric separable • A configuration of parts within a whole • Bristles - toothbrush • Scene - film • A particular arrangement (not just haphazard) • If components cease to support the overall pattern then different associations may arise – Handle ripped from a door of the car. • No longer a part but a piece 5

functional Material-Object non-homeomeric non-separable • Parts can’t be removed • Capuccino is partly milk • Bread is partly flour • Define what objects are made of. • Component-Integral can be separated – Car without a door handle still a Car • Material-Object can’t – Bread without flour not bread 6

functional Portion-Object homeomeric separable • Cf Material-Object, but parts are the same kinds of thing • Slice of bread is a portion of bread • meter is part of a kilometer • A slice of bread is bread. So slices in a loaf are similar • Portions divided by standard measures – meter/kilometer – hour/day • Selective inheritance of properties • Ingredients of bread are ingredients of slice of bread – But with different quantities • Slice, helping, segment, lump, drop etc. 7

functional Place-Area homeomeric non-seperable • Unlike Portion-Object, pieces cannot be removed • Manchester part of England • Peak part of a mountain • Often between places and locations. • Pieces similar in nature. 8

non-functional Member-Bunch non-homeomeric separable • No requirement for a particular structural or functional relationship • Tree part of a Forest • Employee part of the Union • Ship part of a Fleet • Member-Bunch is not subclass!!! 9

non-functional Member-Partnership non-homeomeric non-seperable • An invariant form of Member-Bunch • Stan Laurel is part of Laurel and Hardy • Fred and Ginger are a dancing couple • Removal of member destroys the partnership – a different partnership may result 10

Summary of Odell’s Compositional Relationships Functional Homeomeric Seperable Component-Integral ! " ! Material-Object ! " " Portion-Object ! ! ! Place-Area ! ! " Member-Bunch " " ! Member-Partnership " " " 11

Non Compositional Relationships • Topological inclusion – I am in the lecture theatre • Classification inclusion – Catch 22 is a Book – It’s an instance of Book, not a part of it, so not Member-Bunch • Attribution – Properties of an object can be confused with composition – Height of a Lighthouse isn’t part of it • Attachment – Earrings aren’t part of Ears – Toes are part of Feet – Sometimes attachments are parts, but not always • Ownership – A bicycle has wheels – I have a bicycle 12

So what? 13

Transitivity X is part of Y, Y is part of Z, thus X is part of Z • We might expect part-whole or composition relationships to behave transitively. – But this is generally only true with the same kind of composition. isPartOf • Engine part of the Car isConstituentOf • Pistons part of the Engine isPortionOf • Pistons part of the Car isMemberOf ... • Sean’s arm part of Sean • Sean part of School of Computer Science • Sean’s arm part of School of Computer Science 14

Transitivity • In partonomies, we may want to identify direct parts – Piston directPartOf Engine; Engine directPartOf Car – Piston is not directPartOf Car, but is a partOf Car • I want to query for all the direct parts of the Car, but not the direct parts of its direct parts. – So directPartOf shouldn’t be transitive • Solution: provide a transitive superproperty Property: isPartOf Characteristics: Transitive Property: isDirectPartOf SubPropertyOf: isPartOf • Queries can use the superproperty to query transitive closure • Assertions use the direct part of relationship • A standard ontology design pattern, sometimes referred to as transitive reduction . 15

Aside: Transitivity and Subproperties • Transitive property R is one s.t. Property: knows for any x,y,z, if x R y and y R z, then z R z Property: hasFriend • Transitivity is not “inherited” by subproperties. SubPropertyOf: knows • Nor is a superproperty of a transitive Characteristics: Transitive property necessarily transitive Property: hasBestFriend SubPropertyOf: hasFriend knows: hasFriend: hasBestFriend: Arthur Beth Charlie Daphne 16

A note on Inverses • OWL allows us to define inverse relationships • hasPet / isPetOf • hasParent / isChildOf • (x R y) iff (y inv-R x) • Be careful about what you can infer about inverse relationships • X SubClassOf (hasPart some Y) – All X’s have a part which is a Y – Are all Y’s a part of some X? 17

Composition • Composition provides a mechanism for forming an object whole using its parts • By considering basis properties if this part-whole relationship, we can identify different kinds of relationship • The different relationships then help us in identifying when, for example, we can (or can’t) apply transitivity. • Explicitly separating these in our representation can avoid incorrect/invalid inferences. 18

Modelling Family History COMP60421 Sean Bechhofer sean.bechhofer@manchester.ac.uk With thanks to Robert Stevens 1

Family History • In Week 1, we had an exercise involving Family History data, kindly donated by Robert Stevens. • The spreadsheet listed people, along with the occupations they held at particular times and where the information had been derived from. • How might we define an ontology to allow us to describe this data? • What are the classes we need to represent? • What are the properties or relationships that we need to describe? • How can we map from the spreadsheet data into some populated ontology? • What queries can we then ask? 2

• Name of Person – Given Name – Surname – Possibly Married name • Date of Birth – If known • Occupation – Year – Source – (Additional Notes) • Sex? 3

Modelling in OWL • Recall that OWL allows us to describe – Individuals. – Classes (of Individuals). – Relationships between Individuals or Properties of Individuals. • What are our Individuals here? • What are the Classes • What are the Properties/Relations? 4

Basic Data • Each Person has – Given Name – Surname – Date of Birth • Some Persons (Women) may also have – Married Surname • OWL provides Datatype properties that allow us to associate data values with Individuals. – Strings, numbers etc. 5

Occupations • We are assuming that we have a hierarchy of occupations or roles (not all of the things that people are listed as doing are necessarily occupations) • This is a simple taxonomy. • We might, at some point, be concerned about modelling this more completely, e.g. through descriptions of the roles, but for current purposes, an asserted hierarchy is fine. • However, a key question is how we associate people with the occupations/roles that they are playing. 6

Modelling Occupations: Attempt #1 Class: Person Class: Role Class: Butcher SubClassOf: Role Individual: W.G.Bright Types: Person, Butcher 7

Modelling Occupations: Attempt #2 Class: Person Class: Role Class: Butcher SubClassOf: Role ObjectProperty: hasRole Individual: Butcher-1 Types: Butcher Individual: W.G.Bright Types: Person Facts: hasRole Butcher-1 8