Non-alternative Artificial and Natural Intelligences Partnership for

Put up Shoot in and Return to Rational Co-evolution with Noosphere

Nicolay Vasilyev

, Vladimir Gromyko

and Stanislav Anosov

Departmen of Fundamental Sciences, Bauman Moscow State Technical University, Second Bauman str., Moscow, Russia

Department of Computing Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

Department of Banking Technology Development, Public Company Vozrozhdenie Bank, Moscow, Russia

Keywords: Evolutional Epistemology, Neurophenomenology, Deep-learned Artificial Intelligence, Consciousness Auto

(Self) – Building, System Axiomatic Method, Language of Categories, Cogno-ontological Knowledge Base.

Abstract: Sophisticated informational resources are poorly supported by semantic assistance. To untwist intellectual

processes under inter-disciplinary activity in computer systems, life-long partnership with deep-learned

artificial intelligence (DL I

) is needed. Resolving universalities problem to acquire knowledge self-

obviousness helps a person to enter hermeneutic circle of noosphere by means of rational auto-poiesis.

Otherwise, genus achievements will remain beyond the powers of the person. Purposeful tutoring allows

transcendental apperception of the third world on the base of super sensual mathematical meanings. System

axiomatic method (AM

) secures true profiling of computer systems and DL I

building. Its adaptive

assistance to subject’s self-reflection in intuitive – discursive forms will apply anthropogenesis laws to

encourage one’s rational consciousness self – building. DL I

implantation leans on cogno-ontological

knowledge base mining. The latter is to be expressed in language of categories playing the role of mathesis

universalis to embrace the variety of theories in their comparative description. Semantic glottogenesis keeps

up the outlook of cognogenesis and will maintain communication on ideas level. The technology is based on

reduction method applied to the person as functional system existing in anthropogenic nature.

1 INTRODUCTION

System-informational culture (SIC) phenomenology

impels one’s thinking-consciousness be in co-

evolution with noosphere and ergonomic changes

(Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2019).

To correspond to scientific complexity of SIC natural

intelligence (I

) is needed constructive evolution as

person’s auto-poiesis (Maturana, Varela, 2001). It is

eurhythmy of idea, intention, and design unity in

consciousness-thinking. Evolutional epistemology

discovered that anthropogenesis exists in the

necessity of adaptive dynamics for knowledge

understanding (Campbell, 2000; Popper, 2002).

Leaning on cognogenesis as objectization process,

philogenesis widens subject’s auto-poiesis. Genus

stands now on the threshold of self-transformation

creating new powerful tool to do it. It can apply DL

https://orcid.org/0000-0001-5880-2143

https://orcid.org/0000-0001-7768-1834

https://orcid.org/0000-0003-3785-2357

to its row. Rational “mutation” on the base of

natural sciences is perspective of bio-socio-cultural

evolution of common sense man. Putting

“reasonable” science at one’s disposal is possible by:

 transcendental reduction: phenomenology of a

person − rational consciousness formation −

happens leaning on mathematical universalities

(MU) for subjective objectization;

 eidetic reduction − intuition phenomenology

(image-idea formation) as thinking primary;

 constitutive phenomenology of glottogenesis

placing meaning in life rang applying image-idea.

Gnoseology is now falsified on the base of

cognition complexity. Therefore, laws of adequate

rational auto-poiesis must be investigated to apply to

DL I

building. Corresponding technology must be

based on MU study. Person’s adaptation to noosphere

complexity depends on human self-development

966

Vasilyev, N., Gromyko, V. and Anosov, S.

Non-alternative Artiﬁcial and Natural Intelligences Partnership for Put up Shoot in and Return to Rational Co-evolution with Noosphere.

DOI: 10.5220/0010297509660973

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 2, pages 966-973

ISBN: 978-989-758-484-8

abilities. Narrow professional orientation restricts

them by calculating and cognitive functions of mind

usage that do not include one into reality of SIC

requiring auto-poiesis to conceive changeable SIC

meanings. Partnership with DL I

is needed to

develop discursive abilities on the base of MU

cultivation and the unity of knowledge formalization

and axiomatization, see Sections 2, 3. Semantic tools

are necessary for it (Gromyko, et al., 2017; Vasilyev,

Gromyko, and Anosov, 2018 – 2020). Our approach

to achieve auto-poiesis is relative to neurophysiology

(Medvedev, 2017) and considerations of brain –

neuro-computer interfaces engineering (Kaku, 2014).

2 NEUROPHENOMENOLOGY

Neurophenomenology puts in order an interface

between “ideal” consciousness and “material”

thinking. It is tuning fork for the row members when

gender achieves obviousness of axiomatic thinking

(cognition) and the row applies self-obvious

axiomatic formalization. As proto-consciousness, a

person is molded according to natural ability of self-

complication and understands the necessity of self-

building. Person brings up his own new organ to

create meanings thus becoming self-conscious of

transcendental transgression to rational

consciousness. Confidence in auto-poiesis possibility

issues from natural fertility of self-development

processes strengthened by scientific thinking

applying constructive self-obviousness of the

abstract. Trend

thinking – cognition – identification –

consciousness must be directed by entelechy of

semantic language usage.

Neurophysiology includes:

 thinking as neuro-networks ergo-mind acting on

the constructive base of idea-image or eidos

(Husserl, 2009);

 ego-person as neuro-networks structural integrity

(consciousness), see Section 4.

Clinical tools to cue brain diseases highlighted the

problem of neurons awakening and the role of ergo-

mind - mistakes detector as “inner” voice to rebuild-

optimize ego – ergo unity. (Medvedev, 2017).

Person = genome & ergo-mind (eidetic neuro-networks)

& ergo-soul (neuro-networks integrity)

& spirit (consciousness of culture)

Figure 1: Person’s neuro-phenomenology.

Consequently, consciousness can strengthen brain

with the help of meaning code and can be regarded on

as real ground giving possibility to control the

material (Kaku, 2014). Constructive boundaries of

real-ideal unity determine neurophenomenology, see

Figure 1. Needed auto-poiesis is connected with the

highest level of nervous system activity.

Cognogenesis, ego-soul integrity, and ergo-mind are

to be used for the modification under the influence of

SIC. Thinking - consciousness is developed on the

way of semantic glottogonia (Pinker, 2013).

Expressing universal essences of mind by means of

MU allows compressing complex knowledge and

making it plain to man. Knowledge substantiation by

MU and AM

application will complement intuition

with convincing tools. Generated in subject’s

memory abiding cognatoms of intellectual processes

will become imprints of these structures for

consciousness building (Vasilyev, Gromyko, and

Anosov, 2019). Glottogenesis transforms phenotype.

Semantic means allow expressing explicitly mind

universal properties. They are to be reflected in

personal cogno-ontological knowledge base

(CogOnt) used by DL I

to see to the subject’s ascent

on meanings. So, ego mind intuition is supported by

ergo structure. Informatics brings formalization in the

form of object oriented approach thus connecting up

language of categories (L

). Man possesses necessary

neuro-complexity that allows untwisting his

intellectual processes up to meaning – transcendation

that has not yet been used in full measure. Entelechy

of consciousness sophistication requires connotation

with DL I

2.1 Universal Tutoring

Thinking in meanings has direct cognitive effect. For

the first time, I

must and is able to support adaptively

gender on the limit of I

abilities. Complexity of

subjective objectization of the third world caused the

wealth of pseudo-crisis psychological phenomena up

to the loss of landmarks in life. But it does not affect

mathematical positions in human intellectual

development due to axiomatic method (AM) of

modeling. As before, computer systems apply

algebraic structures to new phenomena significantly

differing from classical ones. Despite of the fact, the

utmost mathematical abstractions help to untwist

corresponding intellectual processes under new

conditions. Deep–learning of I

and I

will ensure

speculation on new reality. Education must react on

noosphere changes to overcome difficulties exposed

by coming cognitive revolution. Necessary universal

tutoring (T

) must guarantee:

 interdisciplinary activity in SIC;

 man’s adaptation to big data of the third world;

 semantic communication;

Non-alternative Artiﬁcial and Natural Intelligences Partnership for Put up Shoot in and Return to Rational Co-evolution with Noosphere

967

 human life in the virtual worlds of applications.

(Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2020).

Only universally educated person can be adapted to

Internet meanings. Sciences outcome and genuine

rationalism can be used to put up shoot in noosphere.

allows tuning thinking – consciousness processes

to achieve apperception integrity. Partnership

technology with DL I

based on mutual T

pushes

subject to grow naturally into hermeneutic circle to

widen it

(Gromyko, et al., 2017). A person cannot

help thinking. Own complexity identification by self-

reflection and T

transform meanings image obvious

for gender into proto-image self-obvious to a person

due to its description in L

. DL I

will assist man to

identify meanings in symbolic form (Kassirer, 2000).

Adaptive T

will unite inductive real work in

computer systems with scientific ideal presentations

to transform them into “self-obvious” knowledge.

When all is said and done the real and the ideal is the

same synchronized thing (Vasilyev, Gromyko and

Anosov, 2018 − 2019). So, personal transcendence

happens on the basis of universalities problem

solution and semantic glottogenesis (Pinker, 2013).

Origins of meanings birth are to be investigated to

discover underlying universal system properties.

Instead of elements base usage the latter are to be

described in L

admitting their comparative study.

Knowledge formalization uses free mathematical

constructions. DL I

implantation leans on CogOnt

usage as meanings core (Vasilyev, et al., 2018 −

2019). Consciousness dig data are to be factorized by

the meanings to compress knowledge. T

prepares the

work. Meanings genesis is to be used in CogOnt built

in L

and having visually clear form of commutative

diagrams (McLane, 2004).

2.2 System Axiomatic Method

AM gives knowledge presentation by theories. It

marks virtual worlds boundaries. Presentations

objectization occurs with the help of MU. It is result

of algebra, geometry, and analysis synthesis that

attained now formalization. AM is means to conserve

personal integrity under conditions of SIC. Thinking

– consciousness is constantly modified. Sensual

perception and rational scope of the life grounded on

natural sciences(

) exercise influence on the

process. Only AM application has constitutive,

developing effect on a person. AM

causes person’s

auto-poiesis presenting knowledge on meta-

mathematical and semantic levels so as

synchronization of the real-concrete and the ideal-

abstract is needed. Origins are displayed on initial

(Euclid, 1949-1951) and modern AM

(Hilbert,

1948) levels that help adaptively to transform the real

into the ideal and vice versa, see Figure 2:

АМ :

instrumental reality

ideation by axioms

of theories

ideation of modeling

systems description

system meanings

















Figure 2: Axiomatic method levels: from natural sciences

description to semantic in language of categories (L

Geometrical notions are defined by AM itself.

Now in geometry axioms can be expressed in

functional languages (Artin, 1969; Bachman, 1969).

General presentations about space and time are

reflected in ontological essences of continuity and

ordering and strictly defined in mathematical analysis

and algebra. Continuity is outcome of completion

process starting from natural number object (NNO)

that is infinite and perfectly ordered. Incidentally,

natural numbers are regarded on as NNO symmetries.

NNO is extended by means of new ideal elements

coordinated with “old” ones. Natural numbers row N

was subsequently embedded into the ring of integer

numbers Z and into the fields Q, R of rational and real

numbers correspondingly

NZQR

. The

last categorical construction is based on Archimedes’

axiom usage. The process is accompanied by

expansions of initial linear ordering as inheritances

(generalizations) chain

NZQR

OOOO

ordered algebraic systems. Unbroken real numbers

object R is built as Dedekind’s sections of the field Q.

Speaking in L

they are limit cones of commutative

diagrams presented by cones

() { : }

Kq qqq





of ordered set Q. They fill up gaps of the discrete line

Q (Vasilyev, Gromyko, and Anosov, 2019).

Example 1. NNO is also starting point to apply

the same MU of AM

to build the field



()

of p-

additive numbers. A field can be built as factor-ring

if there is any commutative Euclidean’s ring A

and having maximum ideal

IA

. Though initial

ordering of A (if there was any) is sacrificed now but

the field

just the same completion process can

be continued with the help of factor-rings

/ , 1, 2,...

AI k

and next chain of their natural

homomorphisms (Shafarevich, 2001):

( ,...), : / / , 1, 2,...

AI AI k



    

Figure 3 commutative diagram defines limit cone



in the category of rings. All these factor-rings are

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

968

projected



IA

into object



. For any

morphisms

gAI B

there exists unique

one



B

making the diagram commutative:

Figure 3: Projective limit



is limit co-cone.

Universal co-limit object



A inherits arithmetical

operations from initial ring embedded in it



A

by homomorphism

,1,2,...

aaIk 

kernel relation

ker



is zero

{0}

. Ring



abstraction is supported by the next coordinatization



12 1

{ ( , ...) : ( ) }

kk k



    .

It helps to



arithmetic feeling. If

,(),

ZI p

where p is prime then



is ring of integer

additive numbers. It worth mentioning geometrical

meaning of the ring as endomorphisms system of

Abel’s group





1, 1, 2,...



consisting of

the unit circle rotations symmetries. Field



()

p-additive numbers is quotients field of the ring



Objects



,( )

RQZ

can be also built issuing from

analysis usual metric considerations. In difference

from real numbers, p-additive ones are obtained with

the help of

()

closure in non-Archimedes’ norm

|| || || ... || ,

aapap mZ





  





In this presentation

of p-additive numbers

quotients belong to Galois field

()

aGp

. It shows

that ring



has fractal geometrical structure

homeomorphic to Cantor’s perfect set.

3 NATURAL INTELLIGENCE

DL I

building leans on the model of natural

intelligence (I

) as person living in SIC.

3.1 Rational Universality Mind

First of all, subject must possess synoptic view on

natural sciences achievements in their making. Proto-

knowledge of noosphere semantic gives long-term

outlook. Theories dynamics conceals an intention and

origin of idea-thinking to be discovered. Intuitive

objectivity is insufficient for complex science. It is

necessary to master intellectual tools given by strict

linguistic means. Vague humanitarian view must be

replaced by them because forma dat esse rei.

Definition availability signifies existence of a thing

synthetic a priori (Kassirer, 2000). Semantic allows

also getting rid of excessive discursiveness of narrow

specialized rational education. “Algorithmic”

approaches and postponed understanding in teaching

must yield to labour with meanings with the help of

meta-mathematical investigation. They require T

All advantages of humanitarian and rational

origins can be united in super natural knowledge SK

of MU which is synthesis of mathematics,

informatics, and programming. Rational

consciousness self-building needs thinking for

consciousness (Vasilyev N. S., et al., 2018). Maps

universality allows expressing other ones in concise

constructive form (McLane, 2004; Goldblatt, 1979).

Example 2.

Geometry meanings are presented by

different algebraic systems (Artin, 1969). Their auto-

morphisms themselves as space symmetries can be

regarded on as points and lines (Bachman, 1969).

Underlying axioms give origin to diverse geometries

(Hilbert, 1948). Public laughed at Lobachevski’s

“imaginary” geometry considering Euclid’s one as

the only possible. Its existence was proved as soon as

Klein and Poincare constructed non-Euclid’s

geometry models. So, both geometries are consistent.

Riemann’s geometry imparted the space-time unity

with the reality.

Now different theories can be

coordinated by general description and factorization.

Example 3. MU of equivalence relation

RAA

can be regarded on as object

()AOb





of a category



. In L

it is defined as

morphism

:,(,)

CHAC







inverse image.

By means of commutative diagram from Figure 4

equivalence introduces factor-object

Figure 4: Universality of objects

RAR

Non-alternative Artiﬁcial and Natural Intelligences Partnership for Put up Shoot in and Return to Rational Co-evolution with Noosphere

969

New object

/()

AR Ob

possesses universality

properties being Descartes and co-Descartes square

simultaneously (Goldblatt, 1979). Morphisms

(,)





connect pairwise homomorphic

theories presented by objects

. Due to relation

, it is more suitable to work in category



having

objects

{(,)} ()

AAR Ob



and morphisms

(,)







. Each map





transports relation

from object

into object

and answers to some

(,)





. It defines equivalence on

image

()

RR

of relation

. Then

category



can be regarded on as sub-category of

 due to the equality

(,0)



. So, theory A

generalizations are presented by

 objects obtained

as result of factorization

RR R

. In

notations

RK R

and

:/ /

MAK

epi-morphism





makes the next transformation

:( / , / ) ( / , )

MK M M A KK



resulting in the generalizations law:

/(/)/(/ )AK AM K M M

It explains knowledge coordination under

generalizations. In algebraic theories morphism



inverse image

/KM M

is presented by kernel

ker 

in its ordinary algebraic meaning. It is

invariant sub-object

/KM

of object

. So as

invariant objects

KA

then discovered law

takes habitual symmetric form

/ (/)/(/)

KAMKM

Human sophistication occurs with the help of

mind equipping with suitable linguistic forms and

tools. Adaptive help humanizes inevitable intellectual

breaks to be carried into effect under cognition. Direct

problem of education is transcendentality attaining

(Vasilyev N.S. et al., 2018)

. Subject’s working place

(WP) is to be created to cherish and grow up

knowledge about MU though ontological but difficult

for identification and apperception.

3.2 Partnership Is Enough for Mutual

Deep-learning

Being of the second order L

supports reasoning in

functional form. Its great expressive possibilities

ensure strict meta-mathematical investigation to

develop rational objectivity (Popper, 2002). Life in

ideas is as natural as one in emotions. It can be

controlled on WP as “ideated” thinking. Self-

reflecting person will take into account the efficacy

of self-building results. Subject’s auto (self) -

development is secured by DL I

that maintains and

initiates natural processes in his consciousness.

Inverse way of education − generalia praecedunt,

specilia sequuntur gives a person opportunity to

embrace the highest semantic levels of knowledge

(Vasilyev, Gromyko and Anosov, 2018 - 2019).

Subject is able to do it applying AM

of modelling. It

is up-to-date manifestation of without premises

knowledge principle. Besides, person is constantly

influenced by noosphere. Clever tools require clever

users. T

does not pursue the aim to know about

everything but is focused to evolve transcendentality.

Example 4. Orthogonality concept universality.

Meaning of this notion can be depicted in L

. A plane

S symmetries are morphisms of underlying algebraic

system. The maps conserve relations among lines and

points. Orthogonal lines

UV

possess the next

property expressed by commutative diagram from

Figure 5:

Figure 5: Plane SUV .

It describes functor − Descartes product

SUV





(McLane, 2004). Orthogonal lines extend space

dimension and allow introducing Descartes’

coordinates. In non-Euclid’s geometry they define not

one but two interconnected orthogonal coordinates

systems (Kagan, 1949).

Different approaches to the same thing study can

be adaptively singled out by DL I

. It is to a person to

decide on his WP which of them is more suitable for

him. His current intellectual state and attempts to

overcome arising intellectual difficulties are to be

remembered in his personal CogOnt with the aim of

adaptation.

4 PARTNERSHIP TECHNOLOGY

Absence of semantic rational learning is the reason of

modern educational crisis. It will be eliminated by the

technology of partnership with DL I

under T

, see

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

970

Figure 6. Only DL I

can assist man to co-process and

compress semantically big data of Internet files. T

applies AM

using abstract types of data (ATD) for

constructive knowledge presentation. ATD play the

role similar to tools in geometry. Diverse algebraic

systems are general tools of thinking implanted in

program systems in the form of ATD. Auto-poiesis

happens with the help of CogOnt, see Figures 1, 6.

Figure 6: Partnership model.

In distinction to teacher artificial assistant can be

universal and tutor man continuously and tirelessly

using general mathematical tools, see Examples 1, 2,

paying attention to consciousness rationalization.

4.1 Principles of Universal Tutoring

Partnership technology supporting man’s universal

development leans on principal of knowledge without

premises (Husserl, 2009) assuming form of system

axiomatic method (AM

). Its efficacy is stipulated by

principle de docta ignorantia.

Figure 7: Hermeneutic circle of noosphere.

Semantic glottogenesis directs reasoning on the

way of universalities identification, understanding,

and specialization. Man’s self – development occurs

by mind equipping with semantic functional language

(McLane, 2004). Genus has discovered this

mathesis universalis to use for T

, see Figures 6, 7.

This powerful linguistic tool is to remove

discoordination of man’s presentations with the third

world. The latter consists of real documents that are

virtual due to their conceptual complexity.

Functionality of DL I

leans on AM

, L

and meta –

mathematics.

4.2 Neuro Object

It is discovered that thinking as neuro-network

physical processes is unchangeable and similar for all

people. On the basis natural neuro-object (NO

)

embraces meanings applying crossing-over and auto-

folding operations between languages − natural and

. They correspond to knowledge generation and

compression with the help of new concepts, see

Figure 4. DL I

realization can be grounded on the

concept of artificial neuro-object (AO

). The latter is

versatile neuro-network of cognatoms (CogA). Each

of them presents a theory expressed in L

and saved

in CogOnt being dynamic open system. All CogA are

interconnected by functors admitting their

comparison. AO

structure is represented by a graph





, , GVER

. Its nodes are cognatoms, edges

answer to functors, and R is incidence relation among

them. AO

reflects current intellectual state of

subject. AO

growing up is result of person’s

consciousness double helix (CDH) crossing over

processes that are encouraged by I

− DL I

interactions, see Figure 6 (Vasilyev, Gromyko,

Anosov, 2019).

Rational consciousness auto (self) – building is

controllable process. DL I

is answer to coming

cognitive revolution challenges, see Section 2,

Figures 1, 6, 7. From time to time, neural network of

is also compressed in accordance with CDH

auto-folding processes happening in person’s mind.

They are modeled by graph G compression on some

subset of its edges (Tutte,

1984). This operation

corresponds to personal CogOnt factorization

(Vasilyev, Gromyko, Anosov, 2018).

CDH auto-folding accompanies person’s

intellectual breaks connected with meanings

understanding and knowledge generalization, see

Figure 8. For instance, additive category discovery

can be regarded on as result of CDH auto folding on

the basis of correlations among fields, commutative

groups, vector spaces, and modules (McLane, 2004;

Shafarevich, 2001). So, under T

one must carry out

Non-alternative Artiﬁcial and Natural Intelligences Partnership for Put up Shoot in and Return to Rational Co-evolution with Noosphere

971

comparative analysis of different theories (Goldblatt,

1979).

Figure 8: Hermeneutic circle - cylinder of noosphere.

4.3 Cogno: Ontological Knowledge

Base Application

DL I

tutoring uses functor

CogOnt SBD SK

transforming scientific big data of computer

applications into super natural mathematical form.

The functor is to be implanted and take adaptive

personal form PCogOnt used on WP.

Independent vectors idea was born when lines

orthogonality (Ort) was studied, see Example 3.

Afterwards, rectangle was replaced by parallelogram.

Descartes connected number with Euclid’s geometry

thus connecting notion of area with apparent

independent concept of number. In calculus of

segments Hilbert applied finite method (Hilbert,

1948). System of independent axioms (expressed in

) gave him freedom to build different geometries.

Meta-mathematical investigations united geometry,

algebra, and logic.

Mathematics allows doing it now applying AM

, and ATD. Let {f

, f

, …, f

} be any set of elements.

They can be regarded on as generators of free object

D. It means that for any map



there exists unique

morphism



, doing commutative diagram from

Figure 9. Let

ker



is kernel relation in free object

D (McLane, 2004) and

()









Definition 1. Elements

, 1, 2,..., ,

kfi





are

called independent in object

ker



is trivial.

Example 5. Independence concept universality.



Numberofindependent elements is tightly connected

with notion of object dimension. Independence

manifests itself in various ways. Linear independence

(Lin) is identified in Figure 8 if

A

. The objects fall

under the category of vector spaces

VECT

Besides,

...





is Descartes’ product of

spaces

{}, 1,...,

ULinfi k

Figure 9: Free object D.

In category

ING





free object

[ ,..., ]

Px x

is ring of polynomials in k variables

with natural coefficients. According to Definition 1,

system of independent elements

,1,2,...,,

ikf





satisfies to the property

0, [ ,..., ] 0

pspf f







Thus, linear independence is particular case of

algebraic one (Alg).

Maps

1, , ,,2,

fkAi





having the same

domains and co-domains are functionally

independent (Func) if Definition 1 is satisfied in

algebra with operators





(Shafarevich, 2001):

,F co domF dom









Here

...









. Expressions from free

object

are transformed in functions by morphism

: FF









. The property is usually

investigated locally in respective subcategories

SET R

and applied to classes of smooth real-

valued functions in a neighbourhood of a point x

Then functional independence is equivalent to linear

independence of gradients

{()}





. So, maps

system

{}



is functionally independent if

:1: 1F domF co domF



  

In category of casual values (c. v.) CAS free

algebra D consists of all admissible formula in

algebra

{ , ; , 1,..., }

ik 

with signature

corresponding to union and multiplication operations

,

in algebra A, see Figure 9. Probability

distributions

, 1, 2,..., ,



correspond to c. v.

()









. Joint probability distributions

( ,..., )

FFi i

ppx x



and

...

Gi i

pp p

answer



− c.v. images

... , ...

iiii

ffGff



  

The latter is product of partial ones. Only mutually

independent c.v. possesses property



Relation

ker



is trivial only for dependent c.v.

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

972

system. Then Definition 1 singles out dependent

system instead of independent one!

Independence of elements in relational algebra

()REL

means that relation

( ,..., )

rf f





is trivial

if and only if relation



coincides with unit





. Free

object

{ ( ,..., )}

Drf f

consists of language



,, ,,, ,, ,AA



  



 P

terms. In

axiomatic theories dependence means that one of

axioms



can be derived from others.

It is obtained next chain of inheritances

Ort Lin Func CAlg as Rel  

It worth mentioning that Definition 1 leans on other

universalities: product, kernel, and

− unit. Besides,

independent elements allow introducing object A

coordinatization, see Example 3.

5 CONCLUSIONS

System world leading to man possessing second

consciousness is demand on I

transcendental

phenomenology. For noosphere person it is natural to

live in ideas. Info sphere of SIC and I

partnership

with DL I

are to transform thinking on the basis of

ideas images and semantic processes support. Only

then obviousness of natural sciences knowledge will

be returned to self-obviousness of truth. For the

objective, personal working place for universal self-

development is to be equipped by CogOnt for

adaptive cognitive partnership with DL I

and

successful interdisciplinary activity in virtual worlds.

It is person’s irrational destine to achieve auto-poiesis

as outcome of Lamarck’s man-made free evolution

for self-expression in noosphere.

REFERENCES

Artin, E., 1969. Geometric algebra, Nauka. Moscow.

Bachman, F., 1969. Geometry construction on the base of

symmetry notion, Nauka. Moscow.

Campbell, D., 2000. Evolutional epistemology. In:

Evolutional epistemology and logic of social sciences.

Karl Popper and his critics. Moscow.

Euclid, 1949-1951. Elements. Gos. Tech. Izdat, Moscow,

Leningrad.

Goldblatt, R., 1979. The categorical analysis of logic. New-

Holland, Amsterdam, New York, Oxford.

Gromyko, V.I., Kazaryan, V.P., Vasilyev, N.S., Simakin,

A.G., Anosov, S.S., 2017. Artificial Intelligence as

Tutoring Partner for Human Intellect. In: J. Advances

in Intellectual Systems and Computing. 1-st Intern.

Conf. of Artificial Intelligence, Medicine Engineering,

Education. SPRINGER.

Hilbert, D., 1948. Grounds of geometry, Technical

Literature. Moscow, Leningrad.

Husserl, E., 2009. From idea to pure phenomenology and

phenomenological philosophy. General introduction in

pure phenomenology. Academic Project. Moscow.

Kagan, V., 1949. Geometry origins. Tech.-Theor. Litr.

Moscow, Leningrad.

Kassirer, E., 2000. Philosophy of symbolical forms.

Language, University book. Moscow, St.-Petersburg.

Maturana, H., Varela F., 2001. The Tree of Knowledge: The

Biological Roots of Human Understanding. Progress-

Tradition, Moscow.

McLane, S., 2004. Categories for working mathematician,

Physics and Mathematics. Moscow.

Medvedev, S., 2017. Mind vs. brain. Novels on brain.

Boslen. Moscow.

Michio Kaku, 2014. The future of the mind. The scientific

quest to understand, enhance, and empower the mind.

Doubleday, New York, London, Toronto.

Pinker, S., 2013. Thinking substance. Language as window

in human nature, Librocom. Moscow.

Popper, K., 2002. Objective knowledge. Evolutional

approach, URSS, Moscow.

Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2020. Deep-

learned Artificial Intelligence for Semantic

Communication and Data Co-processing. In: J.

Advances in Intellectual Systems and Computing. Proc.

of Intern. Conf. Future of Commun. SPRINGER.

Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2020.

Artificial Intelligence as Answer to Cognitive

Revolution Challenges. In: J. Advances in Intellectual

Systems and Computing. Proc. of 4-th Intern. Conf. on

Human Interaction and Emerging Technologies.

SPRINGER.

Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2019.

Emerging Technology of Man’s Life-long Partnership

with Artificial Intelligence. In: J. Advances in

Intellectual Systems and Computing. 4

Future

Technologies Conference. SPRINGER.

Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2019. Deep-

Learned Artificial Intelligence and System-

Informational Culture Ergonomics. In: J. Advances in

Intellectual Systems and Computing. 10-th Intern.

Conf. on Applied Human Factors and Ergonomics.

SPRINGER.

Vasilyev, N.S., Gromyko, V.I., Anosov, S.S., 2018. On

Inverse Problem of Artificial Intelligence in System-

Informational Culture. In. J. Advances in Intellectual

Systems and Computing. 1-st Inter. Conf. on Human

Systems Engineering and Design. SPRINGER.

Shafarevich, I. R., 2001. Main notions of algebra, Regular

and chaos dynamics. Izhevsk.

Tutte, W.T., 1984. Graph Theory, Addison-Wesley.

Massachusetts, London.

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