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Brain and Artificial Intelligence

Ángel Garrido
Faculty of Sciences, National University of Distance Education,

9 Senda del Rey, Madrid 28040, Spain
Tel. +34 91 398 86 90 / 71 13

agarrido@mat.uned.es

Abstract
From ancient times, the history of human beings has developed through a succession of steps

and sometimes jumps, until reaching at the relative sophistication of the modern brain and culture.
Researchers are attempting to create systems that mimic human thinking, understand speech, or beat
the best human chess player. Understanding the mechanisms of intelligence, and creating intelligent
artefacts are the twin goals of Artificial Intelligence (AI). Great mathematical minds have played a
key role in AI in recent years; to name only a few, Janos Neumann (also known as John von
Neumann), Konrad Zuse, Norbert Wiener, Claude E. Shannon, Alan M. Turing, Grigore Moisil,
Lofti A. Zadeh, Ronald R. Yager, Michio Sugeno, Solomon Marcus, or Lászlo A. Barabási.
Introducing the study of AI is not merely useful because of its capability to solve difficult problems,
but also because of its Mathematical nature. It prepares us to understand the current world, enabling
us to act on the challenges of the future.

Keywords: Classical and Non-Classical Logics, Fuzzy Logic, Uncertainty, Brain, Networks,
Artificial Intelligence, Neuroscience.

Motto: Everything is vague to a degree which you do not realize until they have tried to

specify. (Bertrand Russell, 1923)

1. Introduction
The historical origin of Artificial Intelligence as a scientific field was established at the

Darmouth Conference (1956). In that year, John McCarthy coined the term, defined as “the science
and engineering of making intelligent machines”. But this definition does not cover the actual
breadth of the field. AI is multi-connected with many other fields, such as Neuroscience or
Philosophy; and we can trace its origins further back, to arcane origins, perhaps to Plato, Raymond
Lully (Raimundo Lulio, in Spanish), G. W. Leibniz, Blaise Pascal, Charles Babbage, Leonardo
Torres Quevedo, etc., with their attempts to create thinking machines. A suggestive definition of the
field would be to say that it is the area of Computer Science that focuses on creating machines that
can engage on behaviors that humans consider intelligent.

The history of AI field is long and fruitful; just recall topics as diverse and important as the
famous Turing test, the Strong Vs Weak AI discussion, the Chinese Room argument, and so on. And
modern AI has spanned more than fifty years now.

We know the origin of ideas about thinking machines and the mechanisms through which the
human brain works; the possibility of mimicking their behavior if we create some computational
structure similar to the neuron, or perhaps the neural system, its synapses or connections between
neurons, leads to the production of what is called a Neural Network.

The central purpose of AI would be to create an admissible model for human knowledge. Its
subject is, therefore, “pure form”. We try to emulate the way of reasoning of a human brain.
Research directed towards this goal can only happen in a succession of approximated steps, but the
attempts proceed always in this sense.

Initially, AI worked over idealizations of the real world. Its natural fields were, therefore,
“formal worlds”. Search procedures operated in the Space of States, which contains the set of all
states (or nodes, in the case of representation by graphs), that we can obtain when we apply all the
available operators. Many early AI programs used the same basic algorithm. To achieve some goal

BRAIN – Broad Research in Artificial Intelligence and Neuroscience, Volume 8, Issue 4 (December, 2017),
ISSN 2067-8957

(winning a game or proving a theorem), they proceeded step by step towards it (by making a move
or a deduction each time) like searching through a maze, backtracking whenever they reached a
dead end. This paradigm was called “reasoning as search”.

2. Connection AI - Brain
Studying Artificial Intelligence is interesting not only because of its potential to tackle many

open problems, both inside the field and in application to others scientific areas, and even in the
study of the Humanities, but also because it is a new and very creative branch of Mathematics, and
it prepares us to understand the current world, enabling us to act on the challenges of the future.

“An artificial human brain can be built within the next ten years”, said Henry Markram,
Israeli-born scientist, professor at the Polytechnic of Lausanne and director of the Blue Brain Project
(BBP), also called Human Brain Project.

BBP: This is a project by the Swiss government, and also funded by private donations, with
the aim of trying to build an artificial copy of the mammalian (and therefore human) brain. In 2013
many euros were assigned to this project (and another on graphene) for research over the next ten
years. Turning to this Project, Prof. Markram’s team is concentrated in the study of the `neocortex´,
which is the layer of the brain responsible for higher functions directly, like, for example, the
conscious thought. In recent years, this team has managed to decipher the structure of the
`neocortical column´. By working with a software model that reproduces tens of thousands of
neurons, all different from each other, they managed to create the artificial brain. All this opens up
new and promising perspectives for science in its support for improving the lives of humans. We
would need a laptop for each neuron. Therefore, ten thousand laptops are needed. So this team will
use an IBM supercomputer with ten thousand processors.

Through simulations we can observe brain function and behavior in dysfunctional situations,
as in the case of depression or Alzheimer. The tool will be able to understand what happens in the
brain and may try different behaviors. It's like in aeronautics: a model simulates the flight and can
test how it would be affected by wind, rain and other weather conditions, and how they respond to
the aircraft. Now they are trying to do something similar with the brain. It is expected that in the
future, neuroscientists know how the brain is formed, develops and ages, or the mechanisms by
which we learn and improve our intellectual capacities.

We should also mention another program, somewhat parallel in purpose to the previous,
which is the American BRAIN project. Their budget is for a similar amount, and aims to emulate the
achievements of the Human Genome Project. It can be seen as a kind of `spatial´ new career, but
now between Europe and the USA. The map of the brain will be built thanks to these new
`cartographers´ of neuroscience, an initiative that will see its results in the coming years. Very big
companies like Google, IBM, or Microsoft collaborated in these projects.

Á. Garrido - Brain and Artificial Intelligence

3. The future of neuroscience
Quantum computing is the `next generation´ of technology to transform our world. It is

based on quantum mechanics properties that are completely different from the classic ones.
In the world of the smallest particles, we can assume that the laws of nature are frequently

defied. Now, using particles like photons, it was possible to create a new element: the minimal unity
of quantum information, named Qubit (Quantum bit), which allows us to process information so that
if you dedicate centuries of classical computation, it would not be possible. And since the classical
method is linear, in quantum case we can solve more than one operation at a time.

Lately, WATSON has concentrated on other tasks, such as developing new recipes from
existing. Trying to create a mathematical model that allows us to understand cultural evolution is
still a very difficult task, but nevertheless, is starting to be addressed by authors such as Donald
Davidson, Daniel Dennett, as well as some theorist of artificial intelligence. It is a matter then of
growing interest.

4. New applications of fuzzy logic
In Fuzzy Logic, statements are not absolutely true or absolutely false (Dubois, 1980). One

thing can be 5% true (technically, its “degree of truth” is 0.05). Additionally, the variables (or
categories) are no longer numbers and do not have borders linguistically accurate (high or low, rich
or poor, fat or thin, healthy or sick, old or young, hot or cold, etc., depending on the occurrence
degree of these properties), and the operators that modify them are “lot”, “pretty”, “too”, “almost”
or “not too much”. These are called fuzzy modifiers (“hedges” or even “fuzzy modifiers”). This
attributes a value to each of these features diffuse, and that value is accentuated or diluted
accordingly, for example, the various powers or roots of the initial values or with polynomial
expressions that depend on these functions. They are called modifiers “Intensification” or
“Expansion” (Dilation), respectively, with gradual effects and variation. The feature of working with
border regions is not fully defined itself in this area of mathematics (Garrido, 2011).

In 1973, with the basic theory of Zadeh fuzzy controllers, other researchers began to apply
fuzzy logic to various mechanical and industrial processes, improving existing hitherto.

Several research groups have been established in Japan. Thus, Professors Terano and Shibata
from Tokyo, with Professors Tanaka and Asai from Osaka, made major contributions both to the
development of fuzzy logic theory and its applications (Jang, Sun, 1995, 1997).

In 1980 Professor Ebrahim Mandani in the United Kingdom (Mamdani, 1975, 1976, 1977),
designed the first fuzzy controller for a steam engine, which would be applied to control a cement
plant in Denmark, and did-of course-with great success.

In 1987 Hitachi used a fuzzy controller for the Sendai train control, which used an
innovative system created by man. Since then, the controller has been doing its job very efficiently.
It was also during 1987 when the company Omron developed the first commercial fuzzy controllers.
So the year 1987 is considered the “fuzzy boom” due to the large number of traded products based
on fuzzy logic. In 1993, Fuji Fuzzy Logic was used to control chemical injection water treatment for
plants for the first time in Japan. The Fuzzy Technology grew in importance mainly in Japan and
South Korea, having the support of the government, universities and industries. (Sugeno, 1977,
1985).

Parallel to the study of the applications of fuzzy logic, Professors Takagi and Sugeno
developed the first approach to construct fuzzy rules (Fuzzy Rules), from training data or training
(Fuzzy Learning). Since then, the applications of fuzzy logic in everyday life have grown rapidly. In
fact, it is already a part of it. For example, some brands of washing machine using fuzzy logic are
Electrolux, AEG and Miele, and they use these computational methods to moderate the program if
the clothes washing “is not very dirty”, which is a vague concept. The technique is also widespread
in the ABS, braking cars, auto focus cameras, or control of the elevators, spam filters, also called
“spam”, and the now ubiquitous video games. Manufacturers do not want to give much publicity to

BRAIN – Broad Research in Artificial Intelligence and Neuroscience, Volume 8, Issue 4 (December, 2017),
ISSN 2067-8957

the fuzziness involved in these developments for an obvious reason. To say that their cars brake is
controlled by fuzzy logic does not contribute to their sales.

To build a fuzzy system, an engineer might begin with a set of fuzzy rules from an expert.
An engineer might define the degrees of membership in various fuzzy input and output sets with a
sets of curves.

The Fuzzy Rules, or the rules of a fuzzy system, define a set of overlapping patches that
relate a full range of inputs to a full range of outputs. In that sense, the fuzzy system approximates
some mathematical function or equation of cause and effect.

A very important result says that fuzzy systems can approximate any continuous math
function. Bart Kosko (Kosko, 1993) proved this uniform convergence theorem by showing that
enough small fuzzy patches can sufficiently cover the graph of any function or input/output relation.
The theorem also shows that we can pick in advance the maximum error of the approximation and
be sure that there are a finite number of fuzzy rules that achieve it.

Recent advances in Neural Networks, or Neural Nets (in terms of programs that learn from
experience), and Genetic Algorithms (as programs evolve over time) are certainly a fitting
complement to fuzzy logic. Another key reason for increased research in this field would be the
interest in the resemblance between Neural Networks and Fuzzy Systems. The result from analyzing
the relations between these two techniques are Neuro-Fuzzy Systems, which use learning methods
based on neural networks in order to identify and optimize its parameters (Jang, Sun, 1997). Then
appeared genetic algorithms, which together with neural networks and “Fuzzy Systems” are
powerful and therefore are of great interest for future research, both current and mathematics for the
most new, it is already here, quickly taking shape (Sugeno, 1985).

Neural networks are collections of “neurons” and “synapses” that change their values in
response to inputs from surrounding neurons and synapses. The neural network acts like a computer,
because it maps inputs to outputs. The neurons and synapses may be silicon components, or
equations in software, that simulate their behavior.

Supervised learning, reached through supervised networks, tune the rules of a fuzzy system
as if they were synapses. The user provides the first set of rules, which the neural net refines by
running through hundreds of thousands of inputs, slightly varying the fuzzy sets each time to see
how well the system performs. The network tends to keep the changes that improve performance
and ignores the others.

Unsupervised learning, reached through unsupervised neural networks, blindly cluster data
into groups (by a procedure so-called clustering), the members of which resemble one another.
There may be no given right or wrong response or way to organize the data. It is in advance.

Fuzzy Modeling is many times used to transform the knowledge of an expert into a
mathematical model. The emphasis is on constructing a fuzzy expert system that replaces the human
expert, and also as a tool that can assist human observers in the difficult task of transforming their
observations into a mathematical model. In many fields of science, human observers have provided
linguistic descriptions and explanations of various systems. However, to study these phenomena,
there is a need to construct a suitable mathematical model, a process that usually requires a very
subtle mathematical understanding. Fuzzy modeling is a much more direct and natural approach for
transforming the linguistic description into such a model.

5. Fuzzy modeling
A fuzzy model represents the real system in a form that corresponds closely to the way

humans perceive it. Thus, the model is easily understandable, and each parameter has a readily
perceivable meaning. The model can be easily altered to incorporate new phenomena, and if its
behavior is different than expected, it is usually easy to find which rule should be modified, and
how. Furthermore, the mathematical procedures used in fuzzy modeling have been tried and tested
many times, and their techniques are relatively well documented.

Á. Garrido - Brain and Artificial Intelligence

The Fuzzy Logic research continues to advance in the leading countries (Zadeh, 1975, 1988,
1989) in terms of economic and technical progress, as well as in less advanced countries, such as
Spain. But groups that have formed attempt to advance our science in this direction, as well as on
deep (on mathematical foundations and philosophical) theoretical consequences, which influence
the future challenges (Garrido, 2011, 2017).

It must be stated that there has been some important progress when it comes to the
Aggregation Operators (T-Norms, T-conorms, and so on) in Fuzzy Modeling. Alongside all this
development, new generalizations of the existing mathematical theories will come to create a new
science, which will apply a lot more to our reality.

It is also important to note that fields apparently far enough outside of the treatment of
fuzziness, such as the symmetry and the entropy, have entered into new avenues of research by
Fuzzy Symmetry, the Fuzzy Entropy, the Fuzzy Graphs, and so on (Garrido, 2014, 2015, 2016,
2017).

There are more and more applications of all the new branches of Artificial Intelligence and
Robotics. Among the most outstanding, we have the investigations carried out under the direction of
Professor Doctor Manuella Kadar, with a view on the automation of the industrial processes of
ceramic production, in the region of Transylvania. It has the support of European Union funds. In
this team is integrated the author of this article.

Acknowledgement
This work was supported by a grant of the Romanian National Authority for Scientific

Research and Innovation, CNCS/CCCDI –UEFISCDI, project number PN-III-P2-2.1-BG-2016-
0333, within PNCDI III.

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Angel Garrido (b. July 10, 1956) received his BSc in Pure Mathematics, MSc in Computer Science

(1979), PhD in Mathematical Logic and Computer Science, with Summa Cum
Laude, First Extraordinary Price of Doctorate, by UNED. Now he is Permanent
Full Professor of Mathematical Analysis in Department of Fundamental
Mathematics, Faculty of Sciences, at UNED. Gold Medal at the `Vasile
Alecsandri´ University of Bacau, Romania. His current research interests include
very different aspects of Artificial Intelligence and Fuzzy Measures. He has
authored 2 books and 248 published papers, with more than 50 participation in
high level conferences, being a member of International Program Committee of

32 conferences and workshops, Editor-In Chief of AXIOMS, Guest-Editor of SYMMETRY, and
many other journals.