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Sense Theory
(Part 3)
Sense Derivative
[PS Standard]
Egger Mielberg
egger.mielberg@gmail.com
07.02.2020
Abstract.
In an attempt to create a theory for describing such a human phenomenon
as a possibility to selflearning, we need to create an instrument for
dynamic modeling of sensetosense (S2S) [3] associations between
heterogeneous objects. This instrument would help understand the nature
of the causetoeffect relationship [4] and the creation of new knowledge.
In this article, we describe one of the instruments, sense derivative, that
sheds light on the nature of forming new knowledge in the field of Artificial
Intelligence.
1. Introduction
In traditional mathematics, the derivative of a function of a single variable
(multiple variables) measures sensitivity to changes of one variable (many
variables) towards another one. In Sense Theory, the derivative of a sense
function [2] measures sensitivity to propertychanges of one NoSense Set
of the object towards sense changes of this object. Also, it clearly shows
sense associations between objects of different nature.
Compared with trillions of synaptic connections in the human brain, the
sense derivative allows a researcher to analyze trillions of possible sense
connections. So a NoSense Set of nmeasurement may include
possible sense objects.
2. Problem
Like in traditional differential calculus, in Sense Theory we need to
formulate a mechanism of changing (sense constituents) on NoSense
Set . In other words, we need to be able to define sets (subsets) on
which the sense limit is:
1. always constant
2. absent
3. divergent
In practice, a set on which the function is defined may as increase as
decrease. For these situations, we need to describe a derivative on union
(set increasing) and a derivative on disunion (set decreasing). Both
derivatives form a new knowledge.
Also, each object has a series of key properties that define it uniquely. For
this case, we will describe a derivative on property.
3. Solution
Derivative on union.
Let's to be defined on the set of or . Then for any ()
defined on ( ), semantic derivative ( ) on union is
or
,
where K < M, M > L.
The equivalent form is
Unlike semantic derivative on disunion, NoSense Set of on union
can be put as on the left side as on the right side from the operator of
semantic union as
Axiom (Sense Limit of Derivative):
“The semantic derivative on union has two cases:
1. the sense limit is defined:
2. the sense limit is undefined:
”
Properties:
1. ,
2. ,
where
or
3. ,
where
or
4. ,
if
5.
where
6.
7.
where
Derivative on disunion.
Let's to be defined on the set of or . Then for any ( )
defined on ( ), where M < N, semantic derivative ( ) on
disunion is
or
,
where N > K.
The equivalent form is
It is important to remember that NoSense Set of is always put on
the left side from the operator of semantic disunion as
Axiom (Constancy of Sense Limit):
“The semantic derivative on disunion of function defined on set of
has always a limit if and only if the derivative on object of is defined for
each element of , then:
”
Properties:
1. ,
2. ,
where
or
3. ,
where
4. ,
if
5.
where
6.
7.
where
Derivative on property (disunion).
Let's to be defined on the set of or . Then for any ()
defined on ( ), where M<N and MN, semantic derivative (
) on on disunion is
,
where – iproperty of ,
.
The equivalent form is
.
Properties:
Items 1, 2 and 3 is identical to the derivative on disunion if the
following requirements are met:
4. , .
5,7. , .
6. .
Derivative on property (union).
Let's to be defined on the set of or . Then for any ()
defined on ( ), semantic derivative ( ) on on union is
,
where – iproperty of ,

where
– sense punctured neighborhood.
The equivalent form is
Properties:
1, 2, 3: :
,
4. , :
:
.
5,7. , :
:
, :
.
6.
.
Derivative on object (disunion).
Let's to be defined on the set of or . Then for any ()
defined on ( ), where M<N and MN, semantic derivative (
) on object on disunion is
,
where
.
The equivalent form is
.
Properties:
1. .
2. ,
where
3. ,
where
4, 5, 6, 7. Evident, based on derivative on disunion.
Derivative on object (union).
17 properties is being derived by the rules for the derivative on
object (disunion).
4. Conclusion
In this article, we presented the instrument for dynamic modeling
of sensetosense (S2S) [3] associations between heterogeneous
objects. It will help better understand the nature of the sense
constituent of the object.
We hope that our decent work will help other AI researchers in
their life endeavors.
To be continued.
References
[1] E. Mielberg, “Sense Theory, Part 1”, 2018, https://vixra.org/pdf/1905.0105v1.pdf
[2] E. Mielberg, “Sense Theory. Sense Function, Part 2”, 2018,
https://vixra.org/pdf/1907.0527v1.pdf
[3] E. Mielberg, “Arllecta: A Decentralized SenseToSense Network”, 2019,
https://osf.io/5ag8d/
[4] E. Mielberg, “Decentralized Chain of Transactions”, 2018,
https://vixra.org/pdf/1904.0064v1.pdf
[5] G. Stang, “Calculus”, MIT,
https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf
[6] L.H. Loomis, S.Sternberg, “Advanced Calculus”, 1990,
http://people.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf
[7] G. Osborne, “Differential and Integral Calculus”, 1906,
http://library.umac.mo/ebooks/b31290735.pdf
[8] V. Jungic, P. Menz, R. Pyke, “A Collection of Problems in Differential Calculus”,
2011,
https://faculty.ung.edu/jallagan/Courses%20materials/Math%201450%20Calculus%201/
Syllabus%20and%20ebook/problems%20and%20solutions%20for%20calculus%201.pd
f
[9] M. Bittinger, D. Ellenbogen, S. Surgent, “Calculus and Its Applications”, 2012,
https://www.sac.edu/FacultyStaff/HomePages/MajidKashi/PDF/MATH_150/Bus_Calculu
s.pdf
[10] J. Erdman, “Exercises and Problems in Calculus”, 2013,
http://web.pdx.edu/~erdman/CALCULUS/CALCULUS_pdf.pdf