Fabian M. Suchanek
Knowledge
Representation
70
We want to be able to represent any possible bit of knowledge
about the world in a computer. No easy feat:
Goal: Make computers understand
2
—
industry experts from Google, Microsoft, Facebook, Amazon, IBM
Knowledge representation is a difficult skill to learn on the job. [...]
The importance of knowledge representation in diverse industry
settings [...] should reinforce the idea that knowledge representation
should be a fundamental part of a computer science curriculum as
fundamental as data structures and algorithms.
Here, we look at the knowledge representation formalism
that has evolved as a standard in the domain.
Overview
3
•
Entities
•
Classes
•
Relations
•
The gory details
•
Reification
•
Canonicalization
•
The Open World Assumption
•
Reality
An
entity
(also: resource) is any particular object of the world
or imagination, be it abstract or concrete.
Entity
4
(The exact definition of “entity” is a philosophical conundrum. Don’t worry about it for this course.)
>digression
Digression: Entities
5
Is this an entity?
How many entities are there?
Or this?
Digression: Entities
6
Is this an entity?
How many entities are there?
Or this?
Isn’t everything just atoms?
>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
7
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
8
Humans replace their cells every 7 years.
see: Theseus’s ship on Wikipedia
A KB usually contains only a finite set of entities that are of interest, and it
assumes them to be atomic and identifiable.
An
identifier
for an entity is a string of characters
that represents the entity uniquely in a KB.
Def: Identifiers
9
Examples for identifiers:
• unique names, as in YAGO or DBpedia:
Elvis_Presley_(singer)
• abstract identifiers, as in Wikidata or Freebase:
/m/02jq1
We sometimes say “entity” when we mean the identifier. We sometimes use images for the identifiers.
Try it out!
An
label
for an entity is a human-readable string that names the entity.
Labels that refer to the same entity are called
synonyms
.
Entities that have a label are called
named entities
.
Def: Labels
10
identifier (for a named
entity, Elvis Presley)
labels
(all synonymous)
[Elvis on Wikidata]
A label that refers to several entities is called
ambiguous
.
Def: Ambiguity
11
Example: “Paris” is an ambiguous label, as it can refer to
several cities, a greek hero, or people with that name.
Paris reads about Paris in Paris.
Try it out!
Identifier:
Paris_Hilton
Paris_(Greek_myth)
Paris_(city)
Labels:
“Paris Hilton”
“Paris Whitney Hilton”
“
Paris
”
...
“Paris the Hero”
“
Paris
”
“Alexander”
...
“
Paris
”
“City of Light”
“Parigi”
...
>literals
A
literal
is a fixed value that takes the form of a string of characters.
(It is an entity that is identical to its identifier — in all KBs.)
Def: Literals
12
"1935-01-08"
"Hello world"
"42"
This is the number 42,
and any KB will use the identifier "42"
to refer to this entity.
Overview
13
•
Entities
•
Classes
•
Relations
•
The gory details
•
Reification
•
Canonicalization
•
The Open World Assumption
•
Reality
A
class
(also:
concept
) is a set of similar entities. Each entity is an
instance
of (also: has the type of, belongs to) the class.
Classes:
- Actors
- Cars
- Cities
- Rivers
- Universities
- Theories
- ...
Class
14
(The exact definition of “class” is a philosophical conundrum, too. See later in this lecture.)
Instances
Class “Actors”
Classes: Example in YAGO
15
[Alizée by Ronny Martin Junnilainen]
[Alizée in YAGO 3]
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
16
type
subclass
subclass
subclass
subclass
subclass
subclass
[Palaiseau in YAGO 4]
>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
Taxonomy: Cheat Sheet
17
>examples
Try it out: city, Elvis, Coli bacteria, Ford, time
Taxonomy: Cheat Sheet
18
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
Taxonomy: Examples
19
iPhone -> smartphone
finger -> hand
apple -> orange
flower -> plant
Paris -> city
fruit -> food
France -> Europe
Paris -> France
city -> country
Taxonomy: Examples
20
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”?
21
maleAnimal
femaleAnimal
cat
animal
subclassOf?
subclassOf?
subclassOf?
subclassOf?
Taxonomy: Examples
Consider a taxonomy of the animal kingdom.
How do we deal with “male” and “female”?
22
Taxonomy: Examples
maleAnimal
femaleAnimal
cat
animal
femaleCat
Overview
23
•
Entities
•
Classes
•
Relations
•
The gory details
•
Reification
•
Canonicalization
•
The Open World Assumption
•
Reality
A relation is like a table.
Intuition: Relations
24
Person
City
Year
Atkinson
Consett
1955
Monroe
Los Angeles
1926
...
Relation “born”:
A
relation
(also: predicate, relationship, property) 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
25
>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
26
The semantics/denotation of a symbol is
the “meaning” of the symbol,
i.e., the real world entity or tuples.
Digression: Semantics
27
Syntax
Semantics
But these are again symbols.
What is their semantics?
Digression: Semantics
28
Digression: Semantics
29