With this comprehensive breakdown of abstraction's multiple layers and components, we can understand and answer the question if abstraction is essential to artificial intelligence. Lorenza Saitta, Università del Piemonte Orientale

1. Is Abstraction a
Key to Artificial
Intelligence?
Lorenza Saitta
Università del Piemonte Orientale
lorenza.saitta@uniupo.it

2. Premise
« Is abstraction a key to computing? »
[Kramer, 2007]
The same question can be posed for
Artificial Intelligence
« … [the process of] abstraction is the essence of
intelligence and the hard part of the problems being
solved »
[Brooks, 1991]

3. Representation
• Representation is critical in AI tasks
• Search for the “best” representation
• One that facilitates performing a task/solving a problem
• Often difficult to know a-priori which is the best
representation
• Expert definition on the basis of domain knowledge, experience,
analogy, …
• It is important to be able to easily change
representation when needed
• Several types of representation changes have been
proposed in AI à Abstraction is one of them

4. Abstraction = Cognitive Organizational Principle
• Abstraction is a special kind of representation change,
fundamental in human thinking
• Difficult to be precisely defined
• Abstraction aims at reducing the complexity of the
perceived world
« … a ubiquitous function of the cerebral
cortex, one in which many if not all of its areas
are involved, is that of abstraction »
[Zeki, 2009]
“Were it not for the ability to construct useful
abstraction, intelligent agents would be completely
swamped by the real world”
[Russel & Norvig, 2010]

5. Abstraction’s Modus Operandi (1)
• Focalization on relevant information and removal of
irrelevant details
• Aggregation/Grouping
Sciences, notably by Barsalou and co-workers, who provide a theoretical and
an experimental account of the issue [37]. An interesting connection can be
done with Computer Science, namely with the epistemological status of soft-
ware and the basic skills needed for writing good programs6. As a matter of
fact, Kramer wonders whether “abstraction is the key to computing” [272],
abstraction meaning here the capability of removing inessential details and to
identify a common “essence” inside variability.
This capability of going to the core of things is another fundamental aspect
attributed to abstraction, namely the ability to focus on relevance. Objects,
phenomena, events in the world are extremely rich in details and may be very
complex. However, when solving a problem or executing a task, only some
aspects of the reality are useful, and to take into consideration the whole wealth
of details may be confusing. For instance, when planning an aerial trip, the
physical attributes of the aircraft, such as color or exact shape and sizes, are
irrelevant and can be ignored. As another example, in Figure 1.3, a satellite
image of downtown Torino is reported, where the buildings and monuments can
be seen. However, just to find one’s way around the city it is more convenient
to reduce the information to the street network. By citing again Brooks [75],
“... abstraction is the essence of intelligence and the hard part of the problem
being solved”.
Stampa Invia LinkIndicazioni stradali Le mie mappeStampa Invia LinkIndicazioni stradali Le mie mappe
Fig. 1.3: Satellite image of the center of Torino (left): buildings and monuments are visible.
The same area can be described by considering just the street network (right): this abstract
map is more convenient for moving around the city.
Actually, in trying to solve a complex problem it may sometime be a good
strategy to proceed top-down, by starting with a coarse solution and then re-
fining it. At each step of refinement new details are possibly taken into account,
generating a sequence of solutions, each one more detailed than the previous
one. In this case we may speak of a hierarchy of levels of abstraction, with the
6
See Chapter 2.
Part–of
(bicycle)
Member-of
(forest) Functional relation
(computer, tennis set)
Computer
Keyboard
Mouse
Monitor
Body
Floppy
wheel
pedal
saddle handlebar
wheel

6. Abstraction’s Modus Operandi (2)
• Naming Equivalence classes of objects
• Discovery of new concepts
(predicate invention)
Chair =
Object with legs, a seat
and a back
Hub
Community

7. Abstraction’s Modus Operandi (3)
• Building Hierarchies
!
ules into a multilevel pyramid, as illustrated in Figure 1.
At each level, we describe the horizontal relationships
by a network of modules that is by itself the abstraction
of the network at a lower level [3]. In contrast, the verti-
cal relationships, shown as links between layers, repre-
sent the inclusion relationship between modules at
different levels. Using an abstraction pyramid, not only
can domain experts gain a global multilevel view of a
complex system from two different perspectives (hori-
zontal and vertical), but they can also investigate the
interconnection of the modules at a particular abstrac-
tion level of interest in the hierarchy.
abstraction pyramid discovered b
replace the known structure of on
Ontology (GO)), but instead provi
that may be missing. For example
mid identified from a protein-pr
work could illuminate the protein
levels. Some vertical or horizontal
vide additional biological meaning
acterized in the GO’s Directed A
structure.
We divide the analysis of comp
tasks: module discovery and mod
novelty of our two-way approach
synergy of top-down and bottom
rithms. This method identifies m
fashion and constructs a hierarchy
network from the bottom up. In
an abstraction of the network to d
ferent levels in the hierarchy.
divided into three procedures: (1)
mity between nodes; (2) extractin
the network, represented by a sp
partitioning the network based o
(3) generating an abstract network
ing the same procedures to a new
network, we can disclose an a
implied in a complex network. Th
provided in Figure 2 includes the f
Step 1. Input a given network o
Step 2. Calculate the proximit
nodes and use as the link weig
Step 3. Normalize the proxim
z-scores; then discard the links
a specified threshold to reduc
the network.
Step 4. Obtain the maximum-
from the network and use as th
Figure 1 Illustration of vertical and horizontal relationships.
Each circle represents a module. Vertical relationships and horizontal
relationships are denoted by dashed lines and solid lines,
respectively. The thickness of a solid line increases with the
importance of the connection. The original network is at the
bottom (Level 4). Higher-level networks are an abstraction, to a
certain degree, of the next lowest network.
Analysis of Biological Networks
[Cheng and Hu, 1997]
Level of Details (LOD) approach
[Luebke et al, 2003]
s-
C10,
organ

8. Abstraction supports Robust Descriptions
• Reduction of computational complexity
• Increasing in meaningfulness
Volume(x) ≤ a à Bike a < Volume(x) ≤ b à Car Volume(x) > b à Airplane
Has(two_wheels &
open-body & handelbar
& saddle)
-> Bicycle
Has(four_wheels &
body_with_windows)
-> Car
Has(retractable_wheels
& body & wings)
-> Airplane
Task-dependent
Reusable

9. Basic Properties of Abstraction

10. Intensional Notion
122 5 Boundaries of Abstraction
Vehicle!
Land!
Vehicle!
Sea!
Vehicle!
Air!
Vehicle!
Good
transport!
People!
transport!
Cart!Truck! Bus! Train! Car! Bicycle!
…… ……!
AB#918#RS#
AH#708#SW#
BN#387#LG#
…………..#
is-a!
is-a!
is-a!
Instance-of!
is-a!
Fig. 5.2: A possible hierarchical organization of the concept vehicle = “thing used for
transporting people or goods”. Transportation may occur on land, sea, or air. A vehicle
Coverage
Abstraction
Abstraction ≠ Generalization
Less
informative
More
informative
More
general
Less
general

11. Relative Notion
again we do not know what to say: maybe there are important details that the
picture did not capture (for instance, the pistils), or the image is even too much
detailed (maybe, only the perception of a red field, as in impressionist art, would
matter). But, if we look at the picture in Fig. 5.4(b), and we compare picture
!"#$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!%#$
Fig. 5.4: (a) Picture of a poppy field. If we only have this picture, it is impossible to say
whether it is concrete or abstract. (b) The same picture in black and white. By comparison,
this last is less informative than the colored one, because the information referring to the
color has been removed; then picture (b) is more abstract than picture (a). [A color version
Less abstract
More informative
(color information)
More abstract
Less informative
(no color information)

12. Path in an Abstraction Space
“Il vero modo et ordine per dissegnar tutte le parti ie
membra del corpo humano”,
[Fialetti , 1608]
5.1 Characteristic Aspects of Abstraction 127
Fig. 5.6: From Fialetti’s “Il vero modo et ordine per dissegnar tutte le parti ie membra del
corpo humano”, 1608. One among a set of studies for drawing eyes. ( c•
This artwork may
be protected by copyright. It is printed in this book in accordance with fair use principles.)
By taking the top-leftmost and bottom right-most drawings in Fig. 5.6, it
is really hard, without looking at the intermediate steps, to relate them in any
meaningful way. However, the relation between the two clearly appears if we
consider tho whole process of stepwise transformations.
Abstraction has been considered a process also in Mathematics, where the
concept of number is reached, according to Husserl, through a counting process
leaving aside all properties of a set of objects, except their numerosity. Lewis
[299] defines explicitly abstraction as a process of removing details from the
concrete5. Finally, Staub and Stern’s approach to abstraction6 mixes the idea
of abstraction as a process and abstraction as a relative notion, as we do; in
fact, these authors claim that concepts are obtained by reasoning, starting
from the concrete world. Along the reasoning chain abstraction increases, so
that the farther from the concrete world a concept is along the chain, the more
abstract. As an example, real numbers are more abstract than integers. Even
though this approach shares with our view the ideas of process and relativity

13. Path in an Abstraction Space
“Il vero modo et ordine per dissegnar tutte le parti ie
membra del corpo humano”,
[Fialetti , 1608]
5.1 Characteristic Aspects of Abstraction 127
Fig. 5.6: From Fialetti’s “Il vero modo et ordine per dissegnar tutte le parti ie membra del
corpo humano”, 1608. One among a set of studies for drawing eyes. ( c•
This artwork may
be protected by copyright. It is printed in this book in accordance with fair use principles.)
By taking the top-leftmost and bottom right-most drawings in Fig. 5.6, it
is really hard, without looking at the intermediate steps, to relate them in any
meaningful way. However, the relation between the two clearly appears if we
consider tho whole process of stepwise transformations.
Abstraction has been considered a process also in Mathematics, where the
concept of number is reached, according to Husserl, through a counting process
leaving aside all properties of a set of objects, except their numerosity. Lewis
[299] defines explicitly abstraction as a process of removing details from the
concrete5. Finally, Staub and Stern’s approach to abstraction6 mixes the idea
of abstraction as a process and abstraction as a relative notion, as we do; in
fact, these authors claim that concepts are obtained by reasoning, starting
from the concrete world. Along the reasoning chain abstraction increases, so
that the farther from the concrete world a concept is along the chain, the more
abstract. As an example, real numbers are more abstract than integers. Even
though this approach shares with our view the ideas of process and relativity
5.1 Characteristic Aspects of Abstraction 127
Fig. 5.6: From Fialetti’s “Il vero modo et ordine per dissegnar tutte le parti ie membra del
corpo humano”, 1608. One among a set of studies for drawing eyes. ( c•
This artwork may
be protected by copyright. It is printed in this book in accordance with fair use principles.)
Reversible path
Intermediate steps
can be recovered

14. Encapsulation
Q1 = “How many cars are there in the
line ?”
Details of the cars are hidden (they are
irrelevant to the question)
Q2 = “How many red cars are there in the line ?”
Details of the cars must be recoverable
Information is not lost, in the abstraction process, but only hidden,
shielded from the outside view

15. Abstraction Operators
All the operations described can be defined in terms of
Abstraction Operators
Input = I Output = O
O = ω(I,θ)Goldstone and Barsalou [1998]
Giunchiglia and Walsh [1992]
[Korf, 80]
Goldstone and Barsalou [1998]
Giunchiglia and Walsh [1992]
[Korf, 80]
img2 = Thresholding(img1,τ)
Operators are implemented via some algorithms

16. Signals vs Symbols
• Abstraction process always moves from richer, “low-level” descriptions
(concepts) toward “high-level” ones. During the process, only (hopefully)
information irrelevant to the current task is removed from view.
• In particular, abstraction establishes a link between signals (at the lowest
end of the spectrum) and symbols (at the highest end of the spectrum)
• Abstraction acts as a bridge between perceptual processing and symbolic
thinking. It tames the complexity of the sensory input, keeps the important
information, builds up intermediate concepts to reduce reasoning
complexity, and provides us with a re-organized view of the input, ready to
be interpreted in the light of our world model.
• We humans do not ascribe symbolic features to the sensory world, but we
receive raw inputs (images, sounds, …). On the other hand, we do not
interact with sets of weights, but with high level concepts and symbols
• Abstraction allows the early conflict in AI between numerical and symbolic
approaches to be overcome. Both signals and symbols become necessary and
cooperating aspects of both natural and artificial thinking.

17. Acquiring Abstractions
How are abstract operators acquired?
We do not know how we humans do it
Three levels of increasing difficulty
1. Given a set of predefined abstraction operators, we want to
choose the best suited to a given situation
• Usual approach in Machine Learning, Constraint Satisfaction problems,
Planning, Search, Problem Solving, ….
2. Learning an abstraction operator itself
• Some approach in Model-based Diagnosis, Constraint Satisfaction, Planning,
Machine Learning, …
• Deep learning
3. Meta-learning how an abstraction operator can be learned
• This is for the future

18. Deep Learning
Deep Learning
Data
acquisition
Learning
x f(X)
Feature
transformation
Feature
transformation
Feature
transformation
x z1
Classifier
f(X)z2
zh
…....
Intermediate representations
with increasing level of
abstraction and meaningfulness
(hopefully)

19. Learning Object Parts while Classifying
Groups of pixels (motifs) that
occur frequently are memorized
as features and reused in various
parts of an imageExamples of learned object parts from object categories
Learning object parts
Faces Cars Elephants Chairs
Classifier
Parts of objects
Segments
More complete parts of objects
Raw input
ω1
ω3
ω2

20. Local Receptive Fields
• Each feature can connect only to a small region of the lower layer
• (reduction in complexity)
• Similar regions are merged (they share the weights)
• The same features can be detected at different positions in the input
image
• Reduction in the number of free parameters
How can intermediate features be created?
Pooling
• Goal: Robust to local distortion
• Approach: Group similar features together
to achieve invariance
Aggregation
operator
Equivalence
operator

21. An Architecture for Abstraction
• Given a raw input (image, music,
written text, …) consisting of
elementary signals (pixels, sonds,
characters, ...), there are infinite
ways of forming sequences of
intermediate features. Deep learning
uses the output of classification to
select useful features (abstraction
operators, in our language). The
result is task-specific.
• We need a more general guiding
principle:
The best abstractions are those
tha are useful in the greater
number of different tasks
Head
Torso
Arm
Human

22. Evolution
• Multitasks Approach
• It is not possible to handle a large number of tasks at the same time
• A temporal dimension (evolution) has to be added
• A storage to keep the history of learning is necessary
LTM = Repository of
confirmed abstraction
operators and new
concepts
DLk
I O
ωk
1, …, ωk
n
STM ω
ωi
I O
DLh
ωh
1, …, ωh
m
LTM
ωj
ωk
Positive or
negative reinforcement
signal