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The Atom of Knowledge and Science: “A is B”

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Knowledge and information are built up by atoms. This is a small piece of knowledge/ information which after breaking down is not knowledge or information any more.

Printable version: (The Atom of Knowledge and Science 112KB, 6 pages)

This paper presents the view of the author about the existence of the most smallest (tiny) knowledge/ information construction- atom of knowledge. The author claims that any form of knowledge can be serialized up to this atom of knowledge without any lose going through this process. If this knowledge construction is broken down no knowledge/ information is left in its separated or built up in different forms pieces.

1. Atom of knowledge: “A is B”
2. “A is B” and its relations with “A isn’t B”
3. “A is B” and “If A then B”
4. Using eventBased infrastructure in “If A then B” to break it down in “A is B” statements
5. Knowledge to “A is B” form
6. Analysis of the knowledge atom’s truth level (with example)
7. Abstractions in the atom of knowledge are static and unique references
8. Natural language semantics and development concerning “A is B”
9. Citations

Atom of knowledge: “A is B”
There exists a fundamental sole (only one) atom of knowledge. Every form of knowledge can be presented by using only this atom and basic logic constructions without any change of the knowledge while changing its form. Based on this atom of knowledge thoughts are expressed explicitly.

Knowledge is functional description of observed phenomena and their characteristics. It is functional because we use it to determine in which circumstances what important to us changes (happens). Human knowledge only describes phenomena and empirically proves them, it does not have any power to prove theories about phenomena semantics.

The atom of knowledge is the equivalence and has the form of “A is B” statement, where A and B are abstract models of some concepts. Abstract models usually represent only a few functions (behavior characteristics) of the concepts.

A is B
IS is one way function, we can not say that B is A
A, B are abstractions
IS (equivalence) is the product (output) of the process analogy

L: “A is B”
L is the set of “A is B” atoms. Values like <L atom>.A := <some abstractions>; <L atom>.B := <some abstraction>; <L atom>.Truth:= <Boolean>.

People make decisions in their life by analogy, concludes Marvin Minsky (CSAIL, MIT). He makes a review of the most popular classes computer solutions in AI for general tasks from the real life. He claims that discrete logic environment and statistics are not applicable to the common problems of real life.

Here is an example of thinking by analogy. Lets we have two objects/ phenomena A and B for which we know different functionalities, A: w, m, n; and B: m, n. Thus, by analogy B: w, m, n. In other words we accept that the shared functionality between the both objects in m and n is enough in order to conclude equality for w (in A and B), too.

Analogy is a method not only finding final result, but reveals uncertainty in the problem itself. Determining a problem is approximately always engaged with searching information. In such cases analogy is able to give more certainty and transform the problem to already known. Analogy finds claims which after their acceptance can make the task enough certain.

In the nature there is no such thing that to be fully equivalent to another. But the statement “A is B” has in its own mistake not in the equivalence, but in the abstraction of the concepts A and B from the real world (when they are abstracted not from real world concepts, the abstraction can be 100% equal to the real object).

This knowledge atom is tied in groups of atoms (context) and this way forming knowledge statements about concrete phenomena. Sucked out of this group of atoms (out from the context), every atom has a sense of a general statement which is represented like: “Every A is B”, “Every A is every B”, ”A is every B”.

Based on this atom of knowledge thoughts are expressed explicitly. This atom of knowledge represents the way human thinks, by using analogies. Mathematics which is based on equivalence is a prove about the explicit form of expression of thoughts using “A is B”. Having its genesis in the thought about the shared characteristics of two apples and two bananas, Mathematics’ fundamentals are within equality.

“A is B” and its relations with “A isn’t B”
“A isn’t B” can be transformed to “A is B” but not vice versa. Proves of this are first empirical and second this claim is shared by the view about the creative way of human mind processing. If we have knowledge “A isn’t B” we can say that exists “A is B” knowledge and collect a starting point proves on its’ truth having a base the first statement. If we have “A is B” knowledge we can’t say anything about the truth of “A isn’t B” and we can’t be sure about the letter’s objectively full expression (many and different combination of “isn’t” exists with different proves and truth levels). The most general atom of knowledge should be able to be extracted from any existing form of knowledge without lose of information, “A is B” is the form which any knowledge can fully transform to.

“A is B” and “If A then B”
“A is B” is transformable to “If A then B” by insertion of a newly formed variable.
“If A than B” is the first significant form of knowledge in the process of presenting human analytic perceptions. Everything about a phenomena is firstly understood and presented like a behavior. “If A than B” is the first reached complete form of knowledge (such knowledge which can be analysed by mathematics) in the process of examining of new behaviors (functionalities) of unknown and known objects/ phenomena. FSM (Finite State Machine) is the analytic form of “If A than B” knowledge.
After this first stage knowledge is consolidated and abstract ideas are presented (usage of “А is B” form) in order optimization to be implemented where abstractions are connected by analogy to other presented at this moment abstractions to make knowledge “deep”-er (knowledge presentation to be able to not only predict behavior of its object phenomena, but turn it in an environment enabling thinking about the causing circumstances nature of the determined phenomena, which circumstances are invisible while the phenomena has been examined. [1]
“If A then B” contains two conditions. This is one way based on statement construction. Conditions behave the same way as “A is B” does and conditions can be presented as “A is B” sentences. Both have truth levels True, False and Unknown.
A is B => if temp.var.A is A then temp.var.A is B
Doing to opposite transformation from “If A is B” to “A is B” is not enough safe.
If A then B => here A and B are statements and we have two options in examining their objects, if these statements share one object or not.
In general the above statement is like If temp.var.A is sA then temp.var.B is sB. A = (object of A) is sA
After a little reformation:
temp.var.A + temp.var.B = temp.var.AB
If temp.var.AB is sA then temp.var.AB is sB
The last is true reformation, does not lose any information and does not unreasonably add any additional. Virtually merging the objects of the both statements does not produce mistake.
And as a final result:
temp.var.AB is (sA and sB)
This reformation loses a significant piece of knowledge and certainty. It ignores the one way if-then thinking in which A is true if B is true; B is unknown if A is true; A is unknown if B is false or unknown. According to the new form temp.var.AB is sA if temp.var.AB is sB; temp.var.AB is sB if temp.var.AB is sA.

Using eventBased infrastructure in “If A then B” to break it down in “A is B” statements
A is B if B is not C

(“A is B”) { “B is not C” } // the {} brackets means that () is based on the statements in {}

Base on: one statement is base on another when by logical or analogical path the first is derived from the second (statement proving). Often in natural language we use “cause” (“because”) to present this kind of relation.

Base on is one way logical path, if statementA is based on statementB, and when statementA is true doesn’t mean that statementB is true.

People use analogy in order to solve problems. Finding the solution about unknown problem by comparison between the unknown problem with its relevance data and known problems and known solutions. “A is B” is the result (output) of the analogical thinking. We have to say that often analogy doesn’t use the all input data, but in general the data which is different (between the observed cases) when it made a comparison in order to be built an analogy.

Understand: it is revealed when adding or cutting atoms of knowledge from arrays of atoms by informing when a conflict between atoms is happen on the base of their statements.

A is B because B is not C now”

The sentence means in addition that “B is not C” is true:

(“B is not C”) ; ( “A is B”) { “B is not C” }

A is B if and only if B is not C

(“A is B”) { “B is not C” }; (“B is not C”) { “A is B” } – or in an isolated case (no other place clues about these statements’ truth levels are found)

A is B if and only if B is not C

( “A is B”; “B is not C” ) //eventBased relationship technology is applied here. eventBased model is very strong and closely ties its sentences. When one of the statements becomes unknown, the rest are not true anymore- unknown. The all statements have to be true, in order to continue to be true. All statements become false if some of them are false.

This text [2] by engaging proves and analysing them claims that Data Flow Processing, eventBased Algorithms and Data is the right software architecturing trend in Software development, which targets big and too consolidated systems.

Architecture platform is presented which aims to present declarative programming in software products (and in embedded systems, too) which are dependent of asynchronous events (events which moment of occurrence is unknown to the system).
The blog post presents the view of building of eventBased platform which to help its client- developer to declare the relationships between different modules (the relations of modules to variables placed in different ones). The platform recalculates (executes with the update relevant to the module data) the modules when a relevant parameter have changed.
The author believes that the development of a software product must inherit the architecture of a natural science i.e. physics.
There exists a pure scientific basis in the idea of declaring and defining by formula like tiny modules of code. Programming of its own is translation of one real relation into electronic imitation, every natural science do the same thing of translation but modeling abstract information model.

The history of science development goes through such process. Science tries to properly collect and on this to generalize “if-then” statements defining the behavior of a certain class phenomena to turn them into scientific laws (scientific relations between abstract variables) able to predict the behavior of a system in a moment in future.

An example of real life system which is supposed to implement the described eventBased architecture is a space satellite. This is a a big embedded system which needs things to be known in a small amount of time.

Space satellites are embedded systems, which have for a certain period of time to find the most proper solution of an asynchronous occurred problem. If the solution is not proper its implementation can spend resource which is needed for different operation, if the solution is not found within the required period of time the entire satellite is possible to not exist аnymore.
Finding the best solution of a composition of commands (steps) is done by using decision tree, such data structures like which are used in applications for playing chess, which creates of recursive calculation of the possible command (chess move) and the consequences applied to the current situation for every separate possible command. The maximal period of time for choosing a solution and implementing it is supposed to change during the search and implementation of the chosen solution, this period of time is a dependent from the behaviour of outside (external) variables, whose behaviour is asynchronous to the system.
In order to enable the fast creation of this tree, fast computations of resource spending are required, which volume and quality is important to the outside world.
The author imagines single modules determining outside changes and in every such change the physical variable value is computed, which variable can be important to decision making in future. In the blog the author presents a way of enabling this data updates and a parallel adding of new modules and relationships between variables (formulas).

eventBased relationship model enables adding more than 2 statements in one relation like so: (“A is B”; “B is not C”; “B is not D”; “D is not C”)

A is B if B is not C or not C is B or both”

(“A is B”) { “B is not C” OR “not C is B” } //logical statements OR is needed at this presentation

A is B if B is not C and not C is B
(“A is B”) { “B is not C” AND “not C is B” } //logical statements AND is needed at this presentation

Knowledge to “A is B” form
Knowledge in a scientific manner is having an enough full list of the bases of a statement (which are statements or empirical discoveries) in order to be solved problems about the truthfulness of the main statement. Every statement contains only atoms of this kind and every complicated statement can be serialized up to (is constructed of) many “A is B” statements without any lose of knowledge.

Complicated different in their form knowledge constructions can be serialized up to only one equivalence array of “A is B” statements. One array of “A is B” statements can be transformed up to many different in their form complicated knowledge constructions.

A problem to solve of this kind is to find in which conditions (variations of the lists of bases of the statement- true, false, unknown truth levels of the statements in the list) the main statement changes his truth level which is one of these True, False or Unknown. True and False are known logical states of statements, the new state of Unknown is added in order to present situations of scientific uncertainty.

Analysis of the knowledge atom’s truth level (with example)
Abstractions (“A”, “B”) and “is” in the knowledge atom have truth levels.
Truth levels: True, False, Unknown

mainStatement is based on (aStatement1, aStatement2, aStatement3, aStatement4, anEmpiricalDiscovory1) // list of bases of mainStatement

Statements/ Variations aStatement1 aStatement2 aStatement3 aStatement4 anEmpiricalDiscovory1 mainStatement
1 True True False True True True
2 True True False True Unknown Unknown
3 True True False True False False
4 True True False Unknown True True
5 True True False False True False
6 True True True False True False
7 True False True False True Unknown
8 False False True False True False
9 Unknown False True False True Unknown

Table for solving problems. The change in the mainStatement’s truth level as a function of the truth levels of the statements on which it is based on. This is state transition table in the view of mainStatement’s state [3].

And this way for all the 125 (5 statements and 3 possible levels) possible variations of truth levels of all the statements in the base list of mainStatement.

At the view of mathematics analysis main statement can be presented as function and the statements in relation to it as parameters with values their truth levels.

Abstractions in the atom of knowledge are static and unique references
Abstractions are in this case: (called up here “the most tiny”) static and unique reference
unique: to point the reference objects it is only needed and only enough to know this abstraction action.
static reference: nothing within the context is relevant to the action of finding the objects of reference.

“Static reference” and “unique” are synonyms in this case in the view of their concrete behaviour.

(True about approximately all analogies)

Analogy in this case is dynamic. The “is” can be relevant to the context, the first to be a caused by other circumstances placed in the context.

Analogy can be based on some circumstances.

The reference is an empirical method and the analogy is close to it, but not identical to. The reference has not the full functionality of the knowledge atom. The atom of knowledge is related to the concrete topic of the context and is analysable in truth level while the reference is always true and has no direct relation to the case topic, but only indirect providing role.

Natural language semantics and development concerning “A is B”
Every natural word of its own is a declarative calling of a function which works over the “A is B” statements.

Complicated abstractions are references built on analogy and in some cases are too virtual so can not be implemented without additional information to give certainty. Sole natural words (without proper nouns) are analogies out of many references and keep the most important shared characteristics of these references. Word “dog” contains all the shared characteristics of every individual dog no matter its race of distinctive characteristics. Every word as an abstraction can be used in such situations (context) where it’s sole usage is not enough to reach the required at the situation certainty. The abstraction of “dog” used in some cases is an example of such complicated abstraction. The sentence “Have you seen the lost dog?” without any previous information about the particular race and distinctive characteristics of the reference of abstraction “dog” is uncertain.

The above explained abstractions are not static in general because they change with their everyday usage. No matter of the idealize statistical application of every natural word, humans use words which are the most cheapest to use at the particular situation and in fact change the meaning of the used words. By binding the meaning of a word with a concrete phenomena/ characteristic which can at all be not suitable (not best choice) the listeners/ readers of this text learn this new usage as a meaning of the word. It is something not curious while the most important purpose of words is to not be an output of statistical research, but a way to communicate. Communication environment develops by its usage by people and their particular skills of learning to communicate while communicating.

Natural language develops empirically. It is only based on references to actions, characteristics and objects.
Knowledge develops analytically and handles uncertainty. It is based on analogies to important characteristics of phenomena behaviours.

1. Kline, Morris; Mathematics and the search for knowledge
Garabedyan, Garo; Data Flow Processing, eventBased Algorithms and Data


Written by garabedyan

October 13, 2008 at 19:12

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