Semantic Technologies and Applications COMP5860M
John Stell
Room 9.15, School of Computing
j.g.stell@leeds.ac.uk
Lecture 4: February 2020
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Special cases included in the earlier description.
Characteristic Forbidden pattern (Special case)
Functional
Inverse Functional
Asymmetric
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Special cases included in the earlier description.
If this ever happens
Characteristic then this happens too Transitive
There are three other special cases of the pattern to look for in transitivity, but they never need to be checked. Similarly, one for symmetry.
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Characteristics of properties
Examples (explained more in lecture)
property brother hasMother hasParent hasChild ancestorOf sameAgeAs youngerThan isMarriedTo teachesOn
fun inv-fun asymm irr trans symm refl
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Characteristics of properties: EXERCISE
1. Draw a relation with 3 individuals which is functional, inverse functional, transitive, symmetric and reflexive
2. What could be a real-world example of a property that has these characteristics?
3. A relation with 3 individuals with none of the 7 characteristics
4. What could be a real-world example of a property that has
these characteristics?
5. Draw a relation with 3 individuals which is only functional, asymmetric, irreflexive and transitive
6. What could be a real-world example of such a property?
For examples, remember that a property can link things in different classes. In some examples all the individuals might be people, in others they could come from different classes.
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Inviduals can change over time (1)
Time Relation
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fn ifn asy ir tr sy rf
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Inviduals can change over time (2)
Previous slide showed five relations between individuals at different times.
This could be for the property
When you decide what characteristics to put for a property:
You add a characteristic if at EVERY time the relation between individuals has it.
Do not get confused by accidental features that may happen at some times
Ask yourself what are the characteristics (if any) that will ALWAYS be there whatever individuals there happen to be
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Domain and Range
It is possible in Protege to say that individuals connected by a property must belong to specified classes.
We might want to say that a property teaches should be from the class Staff to class Module.
In this case Staff is the Domain and Module is the Range In Protege you can specify the domain or the range as the
intersection of several classes
The Domain and the Range can be the same
– this is NOT the same as the property being reflexive!
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Sub-property and super property
Example:
The motherOf property is a sub-property of parentOf
motherOf ⊆ parentOf If A is motherOf B then A is parentOf B
The parentOf property is a super property of motherOf
In description logic we use ⊆ for inclusion of properties and ⊑ for classes
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Composing Properties (Chains)
In OWL and Protege (but not in lots of other places): Given properties R and S,
R ◦S is the property where x is linked to z if
1. x is linked to something y by R, and 2. y islinkedtoz byS
This is nice for pictures but opposite to the most popular (if misguided) convention for function composition.
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Composing Properties (Chains)
Example
Classes: Module, Student, Degree
Properties: takenBy, compulsoryFor, studiedBy
A module can be studied by a student
A degree can be taken by a student
A module can be compulsory for a degree
How do we say this?
If a module is compulsory for a degree taken by a student then the module must be studied by the student
compulsoryFor ◦ takenBy ⊆ studiedBy
In Protege: studiedBy needs to be a super property of the chain compulsoryFor o takenBy
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Composing Properties (Chains)
The composition or chain compulsoryFor ◦ takenBy is a new property relating every module which is compulsory for some degree to every student taking that degree.
This is a powerful idea. Assuming parentOf, childOf, motherOf, daughterOf have conventional meanings, which of these correspond to or include the properties granddaughterOf, grandmotherOf, siblingOf, grandparentOf, or other easily named things?
childOf o childOf
parentOf o childOf
childOf o parentOf
daughterOf o childOf motherOf o parentOf parentOf o brotherOf
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