Fabian M. Suchanek
Knowledge
Representation
71
•
Entities & Classes
•
Relations
•
Binary Relations
•
Schema
•
Knowledge Graphs
•
Reification
•
Canonic Entities
•
Reality
Overview
2
An
entity
(also: resource) is any particular object of the world
or imagination, be it abstract or concrete.
Entity
3
(The exact definition of “entity” is a philosophical conundrum. Don’t worry about it.)
>digression
Digression: Entities
4
Is this an entity?
How many entities are there?
Or this?
Isn’t everything just atoms?
Digression: Entities
5
Is this an entity?
Or this?
How many entities are there?
>digression
Over time, all parts of a ship are
replaced at some point of time.
Then, is it still the same ship?
see: Theseus’s ship on Wikipedia
Digression: Identity
6
New York Times
Over time, all parts of a ship are
replaced at some point of time.
Then, is it still the same ship?
Digression: Identity
7
Humans replace their cells every 7 years.
see: Theseus’s ship on Wikipedia
A
class
(also:
concept
) is a set of similar entities.
Classes:
- Actors
- Cars
- Cities
- Rivers
- Universities
- Theories
- ...
Class
8
(The exact definition of “class” is a philosophical conundrum, too. See later in this lecture.)
>instances,subclasses
>instances
Entities that are not classes (and not literals, relations, ids) are called
instances
(or
common entities
).
Instances
Class Actors
An entity is an
instance of a class
(also: belongs to a class, has the type, is of the class),
if the entity is an element of that class.
Def: Instance of a class
9
Actor
type
type
A
class
is a subclass of another class, if all instances
of the first class are also instances of the second class.
A
taxonomy
is a hierarchy of classes.
Def: Subclass, Taxonomy
10
type
type
Actor
Person
Politician
subclassOf
subclassOf
type
>examples
If we can say...
• “a/an X”, “every X”
• “Xs” (plural)
• “This is X”
• “X is a Y”
• “Every X is a Y”
then...
X is a class
X is a class
X is an instance of some class
X is an instance of Y
X is a subclass of Y
Cheat Sheet
11
>examples
Try it out: city, Elvis, Coli bacteria, Ford, time
Cheat Sheet
12
If we can say...
• “a/an X”, “every X”
• “Xs” (plural)
• “This is X”
• “X is a Y”
• “Every X is a Y”
then...
X is a class
X is a class
X is an instance of some class
X is an instance of Y
X is a subclass of Y
>examples
Examples
13
iPhone -> smartphone
finger -> hand
apple -> orange
flower -> plant
Paris -> city
fruit -> food
France -> Europe
Paris -> France
city -> country
Examples
14
iPhone -> smartphone
finger -> hand
apple -> orange
flower -> plant
Paris -> city
fruit -> food
France -> Europe
Paris -> France
city -> country
subclass
partof
sibling
subclass
type
subclass
locatedIn
locatedIn
domain and range of “locatedIn”
>examples
Consider a taxonomy of the animal kingdom.
How do we deal with “male” and “female”?
15
maleAnimal
femaleAnimal
cat
animal
subclassOf?
subclassOf?
subclassOf?
subclassOf?
Examples
Consider a taxonomy of the animal kingdom.
How do we deal with “male” and “female”?
16
Examples
maleAnimal
femaleAnimal
cat
animal
femaleCat
A relation is like a table.
Intuition: Relations
17
Person
City
Year
Atkinson
Consett
1955
Monroe
Los Angeles
1926
...
Relation “born”:
A
relation
(also: predicate) over classes is a subset of their cartesian
product. The classes are called the
domains
of the relation.
The number of classes is called the
arity
of the relation.
Def:Relation
18
>digression (tough)
A relation is
any
subset of the cartesian
product. It does not have to correspond to
a real-world relation. Its name is arbitrary.
Digression: Semantics
19
The semantics/denotation of a symbol is
the “meaning” of the symbol,
i.e., the real world entity or tuples.
Digression: Semantics
20
Syntax
Semantics
But these are again symbols.
What is their semantics?
Digression: Semantics
21
Digression: Semantics
22
Linguistic parsing
+ Montague semantics
Digression: Semantics
23
Linguistic parsing
+ Montague semantics
Digression: Semantics
24
One man’s semantics
is another man’s syntax.
All we do is manipulating symbols.
There is no connection to the real world.
Digression: Semantics
25
A binary relation is a relation of arity 2.
For binary relations, the first class is called the
domain
and the second class is called the
range
.
An element of a binary relation is called a
fact
(or: triple),
and we usually visualize it by an arrow:
Def: Binary Relation, Triple
26
bornInCity
The first argument of a fact is the
subject
, the second the
object
.
>events
Every n-ary fact can be represented as binary facts.
n-ary facts as binary facts
27
Wife
Emmanuel
Elvis
...
WEDDINGS
Brigitte
Priscilla
...
Husband
WeddingDate
2007
1967
...
MacronWedding
Emmanuel
Brigitte
2007
husband
wife
date
PresleyWedding
Elvis
Priscilla
1967
husband
wife
date
[
W3C: Defining N-ary Relations on the Semantic Web
]
An
event entity
represents an n-ary fact.
Def: Event Entity
28
Event entity
MacronWedding
Emmanuel
Brigitte
2007
husband
>task
date
wife
Draw a knowledge graph for the following facts.
Irma loves Mr. Bean since 1955.
Mr. Bean drives with Irma to the cinema.
Irma and Mr. Bean watch “Titanic”.
The movie is about the trip of the ship
“Titanic” from Europe to New York.
Task: Event Entities
29
(There may be multiple solutions)
n-ary relations enforce the presence of all arguments:
Binary relations don’t:
Binary relations are flexible
30
born
Person
City
Year
Atkinson
Consett
1955
1955
1955
Binary and n-ary relations can represent the same facts.
• more relations
• less arity
• more flexibility
• less relations
• more arity
• more control
Binary vs n-ary
31
binary
n-ary
>functions
The
inverse
of a binary relation
is a relation
,
such that
iff
.