Functional Programming of Intelligent Systems
V.YU. MEITUS, C. SIMON DE BLAS
Computer Sciences and Statistics
Rey Juan Carlos University
Móstoles, Madrid
SPAIN
Abstract: An intelligent system is a system that uses intelligence to shape its behavior in its environment. This
intelligence depends on the following main factors: the first is the ability of the system to model the environment
with which the system interacts. The second factor: using this model to successfully plan and solve problems that
determine the behavior of the system in the environment in order to achieve the goals set for the system.
Modeling of the environment is based on the use of knowledge about the environment and its components, which
the system collects using its sensors and organs, as well as the knowledge base, which stores information previ-
ously collected or incorporated during the development of the system. This information in the form of knowledge
uses various forms of mathematical structures that form the basis of the model, logic and ontology that are part of
the knowledge representation. Problem solving applies either previous experience, or uses a logical conclusion,
based on the logic embedded in the system during its development, or ontological description, included in the
representation of knowledge and relationships between elements.
When developing an intelligent system, you can apply the methods and tools of functional programming as a way
to represent the development of a particular system, and analyze its capabilities and efficiency at the computational
level.
Key-Words: intelligence, subject area, modeling, knowledge representation, intelligent systems
Received: September 2, 2022. Revised: October 5, 2023. Accepted: October 17, 2023. Published: November 3, 2023.
1 Introduction
Technological support for the process of development
of social structures and their relations always occurs
in leaps that separate one phase of development from
another. In the individual elements of such a struc-
ture, factors are formed that accumulate over time and
then in a relatively short time cause changes, a leap,
a revolution - a transition from one form of struc-
ture to another. This position can be clearly traced
by the example of consideration of industrial revolu-
tions, which determined the natural historical trans-
formation from an agrarian society to a modern soci-
ety, in which, against the backdrop of the fourth in-
dustrial revolution, associated with the transition to
the information society, a new transition, a new social
transformation, has matured and begun. This trans-
formation can be characterized as a transition in all
areas related to the existence of society today, to the
widespread use of technologies and systems that have
intelligence (society 5.0), and the natural transforma-
tion of social relations.
Over time, the processes of spasmodic develop-
ment accelerate. They are usually associated with
new scientific results, engineering solutions and the
formation of new technologies that actively change
the conditions of human existence. Now a new period
has begun, which has arisen in the depths of the infor-
mation society and is determined by the widespread
introduction of artificial intelligence methods and
systems into life, the creation of various intelligent
systems (IS) and the transformation of existing sys-
tems to a new form by adding an intellectual compo-
nent to them. At the same time, IS is understood as
a system that uses representations and methods deter-
mined by intelligence to form its actions and perform
tasks for the solution of which such a system is cre-
ated. Previously, insertion modeling was suggested
as part of the general theory of interaction. In this
models, basic concepts such as environment, agents,
insertion function were introduced, [1], [2], [3]. Other
models that can be viewed as agents interacting in
the environment of distributed data structures based
in macroconveyor parallel computations and insertion
modelling are described in [4], [5] and [6] among oth-
ers. A suitable mathematical structure is suggested in
[7] to abstractly represent a subject area, where a num-
ber of such structures and various variants of logics
are considered.
There are two main approaches to the creation and
development of IS - internal and external. The first,
internal approach, involves a focus on the human user.
Therefore, such systems provide the possibility of
contact and communication with a person on issues
that interest him and which are formulated at the level
of human perception and understanding.
The internal approach includes the directions:
understanding and answers to the questions that
the user puts before the IS in natural language
search and selection of the necessary information
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in the literature and on the Internet, which is re-
lated to the user’s context
creation of an individual information environ-
ment favorable to the user, meeting his interests
and ideas
solving standard tasks that arise for the user in the
process of his interaction with the environment
development of game programs for complex in-
tellectual games (chess, go, poker), IP becomes a
partner of a person
creation of IS, which are trained in the process
of its interaction with the user to the level of a
human assistant
The external approach to creating IS includes the
following directions:
development of IS, the activity of which is com-
parable to human activity in similar conditions or
exceeds human capabilities; this includes various
”smart” systems (home, city, workshop, enter-
prise, car, rocket, unmanned device), as well as
intelligent economic, management and produc-
tion systems
creation of systems that an expert assesses as in-
telligent under the given operating conditions of
the system, including search, decision and ana-
lytical systems, big data processing, predictive
systems
development of IS that replace a person in ap-
propriate conditions, for example, intelligent
robotics, cars and vehicles without a driver
creation of IS, which, after training, perform
work at a level comparable to human activity in
similar conditions
creation of IS based on the definition of the con-
cept of intelligence, which is associated with a
given subject area and successfully solves the
tasks assigned to it in it.
It should be noted that most of these areas are suc-
cessfully developed in various forms, including the
use of multilayer neural networks, which are trained
using enormous amounts of information created and
recorded by man in natural language. Then the col-
lected information is used when it is necessary to an-
swer a question or construct a text that would corre-
spond to some task of the user and be considered as
an answer to his questions.
Similarly, information presented in visual or musi-
cal form can be considered. Then the neural network,
which is the basis for the collection and analysis of in-
formation, creates paintings painted in the style of the
artist on whose work the network was trained, or mu-
sical works of a certain form and type. And even now
it is doing it so successfully that it provokes protests
from the experts on whose works this network was
trained.
The method of creating and training multilayer
neural networks to represent intellectual activity is
undoubtedly promising and extremely successful,
given the size of the network itself and the amount
of information that such a network accumulates and
uses, plus the capabilities of computers that form their
conclusions and suggestions based on this informa-
tion.
An excellent solution was to use for training net-
works millions of literary sources - books, articles,
dictionaries, encyclopedias - which reflect the linguis-
tic representation of various human intellectual activi-
ties, as well as various artistic and figurative represen-
tations of the outside world. The collected and inter-
connected knowledge reflects the common intellec-
tual world of hundreds of thousands of different peo-
ple. This allows us to organize such interaction be-
tween the network and a person at the level of linguis-
tic and figurative representations, which corresponds
to our ideas about intelligence and its capabilities.
At the same time, there is another possibility of
creating an IS, which is based on the definition of the
concept of intelligence and the subsequent considera-
tion of IS as a system that has this property. If such a
definition includes only constructive components that
can be constructed in computer form, then for the cor-
responding subject area it is possible to build an IS in
which the intended intelligence is effectively imple-
mented at the level of the components of the definition
of intelligence. This definition is given in [7]. At the
same time, various options and levels of intelligence
are possible that correspond to this definition.
This allows you to build an IS in a subject area
without being based on a linguistic representation that
is associated with this area. By choosing the main
components for a specific intelligence in a given area,
we obtain different ISs that have different effective-
ness in solving problems in the area under consider-
ation. Moreover, such systems can act intelligently
even in an area for which there is no preliminary de-
scription and which are studied by the IS during its in-
teraction with the area. This approach is relevant, for
example, for systems operating autonomously in sub-
ject areas that differ from each other. Let us also note
that during its development, an IS may contain several
different forms of intelligence at once, and the system
simultaneously solves the same problem in different
ways, comparing solutions with each other.
It is the approach based on the construction of an
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IS based on a pre-selected form of intelligence that is
considered in this work. Moreover, this form of intel-
ligence is characteristic of a person who, for example,
successfully plays certain games that he masters, or is
engaged in certain areas of science, technology, or art.
And it is precisely the focus on a separate subject area
or several interconnected areas that makes it possible
to create separate autonomous objects that have intel-
ligence and apply it in the process of their behavior.
The work also discusses an approach to develop-
ing an IS of this type using functional programming
methods.
This paper is organized as follows: section 2 in-
troduces the basic conditions for intelligence settings,
section 3 provides a definition for intelligence, section
4 introduces a definition for intelligence in functional
programming and section 5 concludes with the impli-
cations of Functional programming of an intelligence
system.
2 Basic conditions for setting
intelligence
To define the concept of intelligence, it is necessary
to first formulate some additional conditions that are
necessary for a further understanding of what consti-
tutes intelligence. There are three such conditions.
The first condition: intelligence is always tied to a
certain subject area (SbA), in which any system en-
dowed with this intelligence operates. “A subject area
is a part of the real, imaginary, or in some other way
given world, environment, environment within a cer-
tain context. The SbA is considered as an integral
part that determines the application of the intelligence
possessed by this system. In this sense, the intellect
of a mathematician differs from that of a composer,
and the intellect of a philosopher differs from that of
a poet. Although sometimes different SbA are com-
bined. Thus, a philosopher may use mathematical the-
ory to express philosophical views and propositions
[8] or use linguistic representation to describe philo-
sophical problems [9],[10].
For example, for an algebraic mathematician, SbA
is a set of algebraic concepts and representations or-
ganized in a certain space and satisfying certain rules
and axioms. In separate subdomains, these concepts
and representations, together with the results obtained
in the form of lemmas and theorems, get their name,
for example, the theory of rings, algebras, groups,
modules. Moreover, any of these subdomains in-
cludes, in particular, such an area as set theory in some
of its representations.
For the intelligence associated with the processing
of texts in natural language, SbA is, firstly, a set of
words, sentences that can be built and are built by a
person from these words, including the final texts that
are made up of these sentences. And secondly, the
set of rules (or possible use cases) that apply when
combining words into sentences, and sentences into
texts.
For the intellect of an artist who paints pictures,
SbA is, on the one hand, the materials, paints and
their combinations that the artist uses when drawing,
and on the other hand, those artistic techniques and
methods by which the artist transfers his idea of the
world to the canvas, cardboard, paper (and, some-
times, wood, brick, glass, porcelain), on which he cre-
ates a drawing or picture. In addition, an essential
role is played by the artist’s emotional state, which he
also conveys in his work, his inner reflection of the
world he represents. These individual, own ideas of
the artist should also be attributed to the SbA. There-
fore, very often different artists actually have differ-
ent ideas about SbA even when they paint the same
woman or the same landscape. And these differences
allow the specialist to understand that the work be-
longs to a particular artist.
It should be noted that along with the natural mate-
rial world, considered as a certain set of SbA (home,
study, work, leisure (theaters, clubs, concerts)), it is
possible to explore the worlds of ideas, ideas, fan-
tasies, beliefs, hopes, virtual constructions. SbA in-
cludes the fields of science, art, management, and pro-
duction. Each of them has its own characteristics and
characteristics - literature, theater, painting, sculpture,
architecture, cinema, those laws and forms, in each
person can realize himself in artistic, scientific, in-
dustrial, technological and other areas characteristic
of modern civilization.
The SbA may include an information base in
which the experience of studying other areas is pre-
sented and accumulated, the knowledge and ideas of
other subjects who have already encountered similar
areas. This information is an additional component
of any SbA and should be taken into account when a
specific SbA is being considered (see Fig. 1). The in-
formation base for each SbA may expand and change
over time, but the general tendency to include possi-
ble variants of information representation in the SbA
remains.
Finally, when considered in relation to a certain
system (subject), an SbA necessarily includes this
system (subject), and possibly other subjects, as its
necessary component. In turn, this addition to the
general SbA, in addition to general knowledge about
the part of space under consideration, contains per-
sonal ideas about this knowledge, its goals, character
traits, individual properties that allow the system to
additionally create its own entities - structures, im-
ages, associations, based on existing general ideas
that are considered in the SbA. At the same time, the
system can influence and change the components of
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Figure 1: Subject Area Representation.
the SbA in order to create new entities in the SbA.
The sequence of actions of the system in the SbA de-
termines its behavior, the result of which should be a
new or modified form of the SbA.
At the same time, the system (subject) has the abil-
ity to perceive both this entity and its individual parts
after each action in order to compare changes in the
SbA with the desired result for this system of individ-
ual actions and all behavior.
It is the possibility of changing the SbA that is de-
sirable for the system that determines the effective-
ness and level of development of the system operat-
ing in this area. And these properties are provided
primarily by the intelligence of the system, which de-
termines what needs to be done or what are the next
goals of the system in the SbA, and what tasks and
in what sequence it is desirable to solve in order to
achieve these goals?
Therefore, the scope of the use of intelligence is
connected with the need to determine the desired be-
havior of the subject (system) that has this intelli-
gence in the considered SbA. This behavior, in turn, is
built through the composition of the results of solving
problems that are defined or that arise in this area in
front of an intellectual subject. Therefore, the second
condition associated with intellect is the determina-
tion of methods for planning and solving problems in
the SbA in which this subject acts, relying on his in-
tellect, to achieve the set goal. What and how should
the subject use to solve the next task?
If we assume that both the task and the solution
of the problem are formulated in the language asso-
ciated with the SbA under consideration, then one of
the possible options for a general approach to solving
emerging problems can be the use of the language of
logic chosen for this SbA. Logic is the science of the
laws of representation of information about the envi-
ronment, operations on this information and composi-
tions of operations that provide means of formalizing
reasoning about some environment based on their in-
formation about it. The conclusion in logic is consid-
ered as a sequence of statements about a given area,
consistent with the laws and rules that determine the
structure of the SbA, which links the initial conditions
and the expected result. In this case, both the condi-
tions and the result are elements of the SbA.
In other words, in such a language or its extension,
first the condition of the problem is presented, then
the transformations that already exist in the SbA, then
the possible result or conditions that this result must
satisfy. Then the solution of the problem consists in
finding a suitable sequence of actions (each of which
is admissible in the SbA), the composition of which
gives the expected solution. From a logical point of
view, it is necessary to build the conclusion of the so-
lution of the problem, based on its condition and the
rules for the conclusion of this logic.
At present, along with classical logic, there are
various non-classical logics, which, in their form and
meaning, are quite suitable for their use in IS. Exam-
ples of such logics, in addition to the logic of pred-
icates, are modal logics, fuzzy, probabilistic, non-
monotonic, descriptive logics, the logic of defaults
and a large number of other logics that are currently
developed in order to bring logical reasoning closer to
the forms and methods used by a person when solving
tasks.
Therefore, the choice of the logic that will be ap-
plied when setting intelligence is considered as the
second condition, which is associated with the pos-
sible solution of tasks that can be put before the IS.
Finally, the third condition associated with the
process of modeling the SbA will be discussed below
in the section on modeling.
3 Definition of intelligence
There are various definitions of intelligence [6], [11],
[12], [13]. But one way or another, all these defini-
tions are related to the ability to solve problems or
determine the behavior of a system, most often at the
human level. This means that there are certain restric-
tions on the perception, memorization and storage of
information about the environment in which a sub-
ject or system endowed with intelligence can solve
problems. In [7], the following definition of intelli-
gence was given. Intelligence, considered as a prop-
erty of a subject or system operating in some SbA, is
determined by the ability, firstly, to model this area,
and, secondly, on the basis of this model, using logic
known to the system to effectively set and solve prob-
lems, the result of which allows the subject (system)
to achieve its goals.
Thus, it is assumed that intelligence allows the sys-
tem to build an SbA model that is adequate to this
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environment, based on its perception of this environ-
ment or the extension of this perception due to in-
formation received earlier and stored in the system’s
memory. This model serves as the basis for the in-
tellect, in which it represents and solves the tasks set
in the SbA for the system and aimed at achieving its
goals in the SbA. Then this solution is transferred to
the SbA, in which it is checked whether the solution
obtained in the model coincides with the expected re-
sult of solving the problem already in the SbA. It is
assumed that the property of intelligence is such that
the model is adequate to the SbA and the solution of
the problem obtained in this way is indeed the desired
solution for the SbA. In the future, a subject or system
with intelligence will be called an intellectual subject
(system).
3.1 Subject area modeling
The process of SbA modeling is an essential part of
the whole concept of intelligence. First of all, because
at the model level all the main processes of solving
problems that are associated with intelligence are per-
formed. And the adequacy of the obtained IS solution
in a real SbA depends significantly on how accurately
the model is built.
There are various methods and ways of modeling
[14], [15], [16], [17]. For example, when a large lan-
guage model (LLM) is considered, the SbA consists
of a set of words that are interconnected by semantic
relationships determined by some contexts. In ordi-
nary language, these relations appear in the form of
sentences. In the case of using a multilayer neural
network, it is trained on a large number of examples
of various sentences that are found in books and ar-
ticles written by people. Connections between words
and groups of words are transformed into numerical
characteristics in the form of neuron weights. Thus, a
model of the language environment is obtained, which
is then used, for example, to answer a question posed
by an IS, which is implemented as a neural network,
or to perform certain tasks (write an abstract, build a
forecast, establish a connection between events). But
this is just a specific example.
On the other hand, an IS may collide with various
objects (OBs), including those for which there is no
large amount of training information. Therefore, an
IS should be able to model any OB that the system
encounters.
“In order to build a model of SbA, first of all,
IS must abstract from reality and create its own idea
of this area, its structure, elements and connections.
Such a representation of the environment is often built
as a set of points, objects (regions) of some space, in
which these points are interconnected by dependen-
cies and relationships defined in this space”, [7].
At the same time, it is assumed that the IS has spe-
cial organs for perceiving information coming from
external objects of the environment. For example, a
person has five senses that allow him to perceive the
environment and adapt to it. But these sense organs
are oriented mainly to the immediate environment in
which a person exists from the moment of birth. In or-
der to expand his understanding of the environment,
a person creates various devices that allow him to
obtain new information about the micro- and macro-
cosm, uses electron microscopes that make it possible
to see viruses, and various types of telescopes to have
an idea of galaxies that are distant from Earth is mil-
lions of light years away.
Therefore, the IS must also have sense organs and
the ability to receive information about the elements
of the SbA, the connections between them, changes
in the area in time and space. Based on these data,
it forms its own idea of the SbA, first dividing it into
parts (structurization of the SbA), then studying each
part, and finally combining such ideas about each part
into a single representation - the synthesis of the SbA
model. In order to perform such a combination, IS
can use some mathematical representation as a ba-
sis, which we will call the supporting structure of the
model. Moreover, for the same SbA, in the process
of its study and use, models can be built that use dif-
ferent carrier structures that represent this area from
a different angle of view (see Fig. 2). For example,
in physics, light can be considered as a wave or as a
particle-photon.
Figure 2: Subject Area (SbA) modelling representa-
tion.
Algebraic, categorical, probabilistic, topological,
fuzzy, computational schemes and representations
can be used as supporting structures for modeling,
[7]. Depending on which carrier structure is used,
we obtain various forms of intelligence, for example,
probabilistic or topological intelligence. Thus, in the
case of probabilistic intelligence, for modeling SbA,
probabilistic representations are used, which make it
possible to describe the properties of objects of SbA
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and the interaction (connection) between them using
probabilistic concepts.
Note that the choice of one or another mathemat-
ical representation for setting intelligence is the third
condition for setting intelligence (the first two were
considered in Section 2).
The process of SbA modeling, which is associ-
ated with the actions necessary to determine intel-
ligence, will be further called intelligent modeling
(IM). This modeling is closely related to the knowl-
edge that the IS accumulates in the process of study-
ing and interacting with the SbA. In other words, at
first the IS accumulates information about individual
elements of the SbA, about the connections between
these elements, and about the actions of some ele-
ments on others, about the structures generated by the
elements in the SbA and stores this information in the
form of a knowledge base about the SbA. In addition,
the IS searches for suitable information about similar
SbA in its knowledge base. For this purpose, knowl-
edge about the general characteristics of those SbAs
in which the given IS operates is stored in the knowl-
edge base.
Then, having accumulated knowledge about what
an SbA consists of, the IS begins the process of IM in
order to ultimately combine and formalize its knowl-
edge in a single subject - a model of a specific SbA.
3.2 Subject area knowledge
The process of SbA modeling, which is associated
with the actions necessary to determine intelligence,
will be further called intelligent modeling (IM). The
general scheme is that the subject represents an SbA
in the form of a knowledge system, which can be or-
ganized as a component of a knowledge base, defined
by a knowledge network or some mathematical struc-
ture, the elements of which are individual knowledge.
Various methods of specifying knowledge are known
in the literature [11]. But, taking into account the ori-
entation towards information systems, in [15] a new
scheme for assigning knowledge, focused on systems
related to intelligence, was presented.
In this case, knowledge about each element or
structure of the X from SbA is specified in the form
of a multicomponent set ζX, which includes a tuple
of features that characterize X and are formed on the
sensory organs of the IS or perceptual means that the
IS possesses. The tuple of features is the first compo-
nent of the set ζX. The second component is a logical
formula that describes element X in the language of
logic, a logical representation of element X. The third
component of the set ζXis a set of connections be-
tween element X and other elements from the SbA.
These three components determine the protoknowl-
edge of the element X. Finally, the fourth component
is an ontology that characterizes the element X al-
ready in linguistic form. The ontological character-
istics of the elements of an SbA make it possible to
operate with an SbA at the level of linguistic repre-
sentations analyzed by a neural network, if necessary.
Another component of knowledge is possible, reflect-
ing the dynamics of element X, if such knowledge is
needed when solving problems of an intelligent sys-
tem.
This modeling is closely related to the knowledge
that the IS accumulates in the process of studying
and interacting with the SbA. In other words, the IS
first accumulates information about the individual el-
ements of the SbA and about the relationships be-
tween these elements, the actions of some elements on
others, stores this information in the form of knowl-
edge about the SbA, and searches for appropriate in-
formation in the knowledge base. Then, having accu-
mulated knowledge about what the ObA consists of,
it starts the process of IM in order to ultimately com-
bine and formalize its knowledge in a single subject -
the SbA model.
3.3 Knowledge about the subject area
There are various options for constructing an SbA
model in the course of IM, [7]. The general scheme
is that the subject represents the SbA in the form
of a knowledge system, which can be organized
as a knowledge base about the SbA, defined by a
knowledge network or some mathematical structure.
Knowledge about each element X from the SbA is
specified as a multicomponent set and consists of at-
tributes, a logical formula that describes the element
X in the language of logic, links between the element
X and other elements from the SbA, and an ontology
that characterizes the element X already in the lan-
guage form. The first three components define proto-
knowledge, and the last one determines the interpreta-
tion of the element X in the ontology associated with
the SbA. Although one more component of knowl-
edge is possible, reflecting the dynamics of element
X, if such knowledge is necessary.
The IM process itself is built as follows:
First, in the SbA, on the basis of the collected in-
formation and data from the knowledge base about
similar areas, the entities of this SbA are distin-
guished, and the corresponding knowledge is associ-
ated with each entity.
Entities in the SbA include:
objects perceived at a given level of perception
as a certain integrity
instances of objects
classes of objects
structures built from various objects, classes
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sets of objects considered and interacting in the
field as a single entity, called an image
connections and relations between objects,
classes, structures, images
processes considered as a successive change of
entities as a result of their interaction or due to
their dynamic characteristics
Then, some subdomains are identified in the SbA
which consist of interrelated entities and have specific
features and features that are characteristic of this par-
ticular SbA and distinguish one subdomain from an-
other. At the same time, it is assumed that the IS has
enough information in the subdomain that can be used
to form the behavior of the system. In other words, a
subdomain is a part of the SbA, analyzed and used by
the IS for planning and determining the behavior of
the system in it.
For example, if a robot is considered as an IS that
can act in various natural conditions and accordingly
orients its behavior to the conditions in which it acts,
then the robot first represents this SbA in the form
of a set of subdomains, and then builds its behavior,
taking into account the detailed features each area.
Each SbA entity is further represented in the form
of knowledge associated SbA with such an entity.
Knowledge about an entity is its representation of IS,
oriented to use when creating an model. In the future,
information will be understood as new information
about the entities of the SbA, received by the IS from
the SbA from the knowledge base or with the help
of the sense organs, appropriate devices, by means
of logical conclusions or hypotheses about the con-
tent, state, and changes of these entities. When con-
structing an IS model of the SbA, information about
the area must be described, structured, associated with
the constituent elements of the external environment
known to the subject (understand the information) and
save this description. Information about the SbA,
which is stored by the IS for further intended or spe-
cific use, is used later in the formation of knowledge
about the SbA, [15].
Knowledge is a representation and a semantic de-
scription of the individual entities of the SbA. Knowl-
edge is used to create an SbA model. Note that in the
absence of knowledge, when modeling an SbA, as-
sumptions, hypotheses about certain entities can be
used. For example, in mathematics, results are some-
times proved under the assumption of the validity of
certain hypotheses that have not yet been proven, but
previously formulated.
There are different forms of knowledge assign-
ment. Next, consider a representation method based
on a multicomponent representation of knowledge.
This representation includes several components in-
troduced and considered in [15]. This variant of
knowledge representation is focused on their use in
the process of SbA modeling, which is necessary for
setting intelligence. This representation uses infor-
mation about the characteristics of the ObA elements
perceived by the subject, the links between them, the
logical representation of each element, and its onto-
logical description. This representation can be ex-
panded by adding a fifth component to the knowl-
edge, which characterizes the dynamic change in the
parameters of an element, for example, its movement
or the change over time of individual links between
elements.
It is assumed that, in addition to the sense organs,
the subject also has a knowledge base (KB), which
reflects his previous experience, or information about
similar SbA, which are already known to the subject
or which he can receive from other subjects. This is
necessary so that the intellectual subject can imme-
diately begin to act, without a preliminary complex
process of mastering an unfamiliar world.
Formally, knowledge ΘAis represented by a
three-component structure of the form ΘA=
(kn(A),A, DA), where kn(A)is proto-knowledge
directly related to the internal representation of the el-
ement and consisting of three components: a set of
features of the object A, a set of links from the object
A to other objects from the SbA, and a logical for-
mula that describes the object A in the logic that is
used by the IS. The set of features of an object is a
set of its characteristics that the IS can receive from
its sense organs, from the tools with which the IS is
armed, and finally from the knowledge base, in which
the experience of both the IS itself and other subjects
who have studied this or similar areas has been accu-
mulated. Descriptions obtained from other informa-
tion sources or relevant literature can be introduced
into the knowledge base. The second component of
proto-knowledge is those relations and connections
that represent the conditions for the interaction of a
given entity A with other entities of the SbA under
consideration. Finally, the third component of proto-
knowledge kn(A)is a logical description of the entity
A within the framework of those conditions and rep-
resentations that can be set in the logic used by the
IS.
The Acomponent is an ontological description
of the object A, focused on a person who controls the
behavior, or on an additional opportunity to obtain the
characteristics of an entity by analyzing its ontologi-
cal description. Finally, the component DAis a set of
operators that characterize the dynamic properties of
the considered object in the considered SbA. For ex-
ample, a robot can move in the SbA while receiving
additional information about its current position and
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state, including possible changes. Or the robot gradu-
ally changes its state, for example, consuming energy
or ammunition.
3.4 Tasks in SbA
The MSbA model is a certain part of the model repre-
sentation space, in which a set of interrelated knowl-
edge about entities (objects, structures, images) exist-
ing in this space is specified, and at the upper level of
the interconnection of subdomains that are included in
the SbA. The model can be associated with a multi-
level map, where the map of each level is a set of iden-
tical, interconnected and interacting entities of a given
area. At the bottom level are objects, at the next level
there are structures, then images, and finally subdo-
mains.
Problems in an SbA are considered either as an ex-
act problem or in a generalized form. An exact prob-
lem in SbA is a pair of entities (A, B), the first of
which A is the condition of the problem, and the sec-
ond B is its result. The expression
(A, B)
itself also includes the formulation of what should be
done as a result of solving this problem, what actions
should be performed by the IS: transform Ainto B,
find the essence of Bin A, include, calculate, derive
or prove the possibility of transition from it to entity
B, and so on.
The generalized task is given as a set of enti-
ties (A1,, An), which should serve as the basis for
achieving a given goal, defined as a part of inter-
related entities obtained from the set (B1,, Bm).
Such a task can be considered as the problem of
achieving some goal determined by the initial entities
from (A1,, An).
The complete solution of the exact IS problem is
defined as a sequence of transformations from the
SbA that allow one to pass from the entity Ato the
entity B. Sometimes one can consider an approxi-
mate solution in which the entity B0is considered as
a solution to the problem
(A, B)
which in a given sense is close to exact result Band
can therefore be considered as a solution. There may
be cases when the desired solution does not exist at
all or cannot be obtained by the means that the IS has.
Note that a variant is possible when the problem
(A, B)is first modified by expanding or supplement-
ing the condition A of the problem to A� and this
completion becomes part of the general problem, and
then the new transformed problem (A0, B)is already
solved.
At the same time, we emphasize that, according
to the assumption, those components from which the
problem solution is built already exist in the SbA,
they do not need to be further defined, but it is de-
sirable to include them in the problem statement in
order to obtain the necessary solution. For example,
it happens that knowledge about SbA needs to be ex-
panded through additional transformations that were
not taken into account in order to obtain a solution to
the problem. So, for example, in mathematics, var-
ious sub-fields of mathematics are often linked to-
gether in order to solve a problem from one area using
the methods of another. Or you need to apply com-
puter technology to analyze a large number of solu-
tions.
In addition, we note that to solve problems in SbA
methods of logic can be used, which is included in the
representation of knowledge, as well as experience in
solving similar problems, which is stored in the KB of
IS. At the same time, it should be taken into account
that individual entities of the SbA can change in the
course of their existence: the task was set under the
same conditions, and after a while not only the entity
Achanged, but also the expected result B, or some in-
termediate entities associated with the solution of the
problem. Taking into account the dynamic nature of
the SbA, we have to solve another problem. And this
feature of IS is very significant. In fact, very often,
instead of solving one IS problem, one has to solve
several interconnected subtasks that take into account
possible options for changing the situation in the pro-
cess of solving the main initial problem.
The problem solving planning process consists in
the initial representation of the SbA in the form of
a certain structure, the elements of which are subdo-
mains, and then the presentation of the existing task in
the form of a set of subtasks, each of which is solved in
its own subdomain. The plan for solving the problem
is built as a plan for connecting the expected solutions
of subtasks in a single solution.
4 Functional IC programming
The development of IS implies the possibility of soft-
ware implementation of such a process as a way to
represent at the program level the main functions and
processes associated with the creation of such a sys-
tem. In particular, such a programming approach can
be effectively implemented at the functional level.
The program representation allows you to model the
behavior and explore the desired system at the level
of its computer form, make the necessary changes and
check the effectiveness of the system before its phys-
ical implementation. This is especially important for
systems that assume rather complex behavior, espe-
cially for intelligent systems, who have intelligence,
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and therefore are capable of demonstrating quite com-
plex behavior.
The creation of an IS assumes that since the
constructed system has intelligence, it must, firstly,
model the SbA that the system perceives and in
which this system operates. And, secondly, using this
model, the IS can plan and solve the tasks that are set
for this system within the framework of a common
goal and for which the system is being developed.
Moreover, the solution process for complex problems
may include a preliminary search for a certain se-
quence of intermediate, auxiliary tasks that need to
be solved before moving on to solving the main prob-
lem - the goal of the system (this is the solution plan-
ning process), then solving auxiliary problems, and,
finally, the transition to solve the main problem.
The modeling process is based on a preliminary
perception of the properties of individual elements
of this area, and the transformation of these percep-
tions into knowledge, which then form the basis of
both the construction of the model and the processes
of solving problems in this model. There are various
options for the transition from perceptions to knowl-
edge. Let’s assume that the set of possible variants
of knowledge is already contained in the knowledge
base, to which the IS has access. In the knowledge
base, knowledge is interconnected in the process of
building the database itself through the use of infor-
mation that is characteristic of objects and structures,
but which cannot be obtained using data from obser-
vation bodies only. Not to mention that the time of
possible observation and identification in real condi-
tions can be very short.
When an IS enters the SbA, it first orients itself
in it, highlighting individual elements and structures
based on the collected features, and then turns to its
knowledge base, which ensures the development of an
IS for a given type of SbA, in order to find matches
with the elements and structures identified in the envi-
ronment. There is a process of recognition and com-
parison of these elements and structures, as a result of
which the SbA modeling is performed, which com-
bines the perception of IS and information from its
knowledge base. These elements, images and struc-
tures are placed in the area of some space associated
with the model, and the area itself is considered as the
carrier of the model with which the IS operates.
Note that in the KB, the basic structure S is first
selected, for each element of which there is a corre-
spondence SbA KB. Then this structure is ex-
panded to the area S0by adding elements to S that are
not directly observed by the IS, but whose existence is
possible based on the experience embedded in the de-
velopment knowledge base. In addition, those trans-
formations and relations are entered into S0, which
are determined on the basis of knowledge about the
constituent elements considered in S0. The area S0
also determines the restriction of the total KB to the
area S0=KB(S0). This limited base, which is tied
to the area under consideration, can be used by IS in
solving problems, especially in conditions of limited
time.
In addition, if individual features of an entity in
an SbA can be determined by direct measurements,
then the possible actions of individual structures and
entities are related to the fact that these entities are
and may not appear during direct observation. At
the same time, these data are usually contained in the
knowledge base as general information about the pos-
sible components of the SbA. Then they are intro-
duced into the logical and ontological components of
knowledge included in model Mof SbA.
For example, for an IS robot, the model is spec-
ified as a multilayer system of maps, starting with
maps that indicate the relative position of objects with
varying degrees of detail in the considered representa-
tion, and ending with maps that show the possible dy-
namics of SbA objects reflected in the information of
the robot. Note that the map can include both a graph-
ical representation of the environment and sets of pro-
grams corresponding to the actions that the robot can
perform in a particular environment.
This model can change dynamically. The changes
themselves can be associated with the properties of
the modeled entities of the SbA, or be determined by
the interactions between the entities and the IS. Or
be refined as a result of additional data that the IS
receives in the course of its actions in the SbA. Dy-
namic changes are associated with a sequence of maps
in which these changes are presented or predicted as
possible or planned states.
For example, if an IS is a robot that operates in
an SbA, then the area itself may change if aerial re-
connaissance means appear in it, or objects that were
absent in the area may appear, or changes may be in-
troduced in the form of new knowledge about previ-
ously defined objects that were absent or disguised.
Considering further the problems of functional
programming, we will focus on the use of Python
language concepts for programming, [18], [19]. The
constituent elements of the model, firstly, are the ob-
jects of the SbA, determined by knowledge about
them. Secondly, the SbA structures, considered as a
set of several interconnected objects, which are deter-
mined by knowledge about the structure as a whole
and act on other entities as a whole. Thirdly, images
are a composite object, in which its constituent ob-
jects set the characteristics of individual properties of
the image, considered as a union of components and
having an integral prototype in a real environment.
Fourthly, subdomains are part of the SbA, including
its individual entities, their dynamics and interaction.
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Fifthly, the processes executed in the SbA.
To specify knowledge about the individual com-
ponents of the SbA and its structures, the IS soft-
ware uses data that is specified in the form of lists and
named dictionaries. In this case, dictionaries may in-
clude names derived from the ontology, which is in-
cluded in the knowledge associated with these com-
ponents. And the corresponding function displays
knowledge about individual entities, structures, im-
ages into the necessary lists and dictionaries. These
lists and dictionaries are then linked into maps as part
of the SbA model.
Note that the structure of knowledge is quite het-
erogeneous, since knowledge includes not only mea-
surable features, but also various expressions - logi-
cal and verbal (ontological). Therefore, both the pro-
cess of modeling an SbA and solving problems in
this model are determined by parallel approaches that
combine logic, language representation, and formal
operations on attributes.
In addition, it should be taken into account that
knowledge about the essence of the SbA may not be
enough, it may turn out to be incomplete, inaccurate,
probabilistic, and sometimes simply absent. In these
cases, it is impossible to construct a unique unam-
biguous model of the SbA. Therefore, hypothetical
variants of knowledge are considered, and for each
variant and hypothesis, its own model is built. Then
we have a multiple representation of the simulated en-
vironment in the form of a set of different variants of
models with different possible entities for which there
is no exact information, but there is an assumption
about what this information can be.
Accordingly, for each version of the model, its
own tasks are solved in parallel, but there is a constant
refinement of the model parameters, the hypothetical
values of those functions and quantities are checked
for which there were no exact data.
If the model has already been built, then the tasks
facing the IS are formulated within the framework of
those entities and relationships between them that are
specified in the built model. The solution of the prob-
lem in this case is considered as a sequence of tran-
sitions between the condition of the problem and the
expected result. Each transition is specified by an ex-
isting transformation that is specified in the model,
and the composition of transformations from the se-
quence of transitions is added to the solution of the
problem. And the complexity of the solution is deter-
mined by the length of the sequence and the order in
which the transformations are applied.
Note that for models that are based on knowledge,
there is a general approach in which the search for
the necessary solution has a number of basic capabil-
ities. In knowledge, there are three different forms of
describing the essences of the SbA and, accordingly,
methods for searching for transformations based on
these descriptions. These forms include:
direct characteristics at the level of signs,
logical description, which involves the use of in-
ference methods to build a solution, and
ontological description, for which the methods of
choosing the necessary transformations are appli-
cable based on methods that are currently widely
used in language models and based on the appli-
cation of problem solving learning methods.
And these forms must be consistent with each
other, and the results obtained from one form are
taken into account when looking for transformations
needed in another form.
Accordingly, for a sufficiently universal IS, pre-
liminary preparation and accumulation of information
is necessary, followed by the creation of a knowledge
base associated with the tasks to be solved, so that on
its basis it would be possible to look for a way to solve
each specific task that can be assigned to the IS in this
particular SbA.
There is also a simpler way, when for a given SbA
and possible tasks of the IS, the classes of tasks that
the IS will have to solve are preliminarily studied and
identified. For example, when the behavior of an in-
telligent robot is considered, it is possible to simul-
taneously consider the range of tasks for which this
robot is created. In this case, the intelligence of the
robot will manifest itself in the way the robot analyzes
and models the environment in which it operates, and
in the breadth of the area of tasks it solves. Since the
robot can combine various tasks, their total number
can be large and quite versatile.
In cases where the classes of tasks to be solved for
IS have already been previously identified, possible
solutions can be prepared for them even at the stage
of IS development. Then the IS, instead of developing
a new algorithm, simply selects the appropriate solu-
tion from the array of existing solutions. Accordingly,
at the functional level, a function is built that maps
the condition of the problem and the expected result
into one of the solutions that are developed in advance
and stored in the knowledge base. In addition, meth-
ods are needed to combine the selected sequence of
solutions, which is determined by the selected tasks
and methods for solving them, into a single path from
the task condition to its result, which determines the
behavior of the IS.
5 Conclusion
An intelligent system is a system that uses intelligence
to shape its behavior in its environment. This intelli-
gence is determined by two main factors: the first is
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the ability to model the environment, and the second
is the ability to successfully plan and solve problems
that determine the actual behavior of the system in the
SbA using this model. Modeling of the environment
is based on the use of knowledge about the environ-
ment and its components, which the system collects
using its sensors and organs, as well as the knowledge
base, which stores information previously collected
or incorporated during the development of the system,
related to possible SbA. In particular, this information
can use various forms of mathematical structures that
form the basis of the model. Problem solving is based
on the use of either previous experience stored in the
IS knowledge base, or is performed using logical in-
ference or other methods, based on the logic embed-
ded in the system during its development, or uses an
ontological description of the problem. Finally, the IS
may try to apply solution methods that have been used
in similar problems, information about which exists in
the system’s knowledge base.
In the future, future research in this direction is
primarily related to the development of certain types
of intelligence associated with various mathematical
structures - topology, probability, fuzzy methods, al-
gebraic structures. In addition, it is assumed that var-
ious types of logic are used as the basis for IS rea-
soning. The ability to communicate with the SbA im-
plies the development and widespread use of specific
research and production systems endowed with intel-
ligence, which should radically change the modern
economy.
If there is a need to quickly create such systems,
then software implementations of their main elements
and associated processes will be required. At the
modern level of presentation, such programs can be
based on functional programming, which assumes the
possibility of a functional representation of the main
processes associated with the actions of an IS and
the use of intelligence when performing operations
that determine the actions of such a system, includ-
ing its modeling and the ability to operate with knowl-
edge that describes the SbA, development of a knowl-
edge base, logic and methods for planning and solving
problems in the model.
Acknowledgment:
The authors would like to acknowledge the help and
support of the Rey Juan Carlos Ukrainian Response
Program for their support.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
V.Yu Meitus carried out the design, Conceptualiza-
tion and Writing - Review & Editing of the paper.
C.Simon de Blas Conceptualization, Writing - Re-
view & Editing and Supervision
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself Rey
Juan Carlos Research Programme
The authors have no conflicts of interest to
declare that are relevant to the content of this
article.
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Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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