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Информация об авторах Зиновий Львович Рабинович – доктор технических наук, профессор, Институт Кибернетики НАН Украины имени В. М. Глушкова, Киев-187, проспект Акад. Глушкова, 40; e-mail: email@example.com Юрий Анатолиевич Белов – доктор физико-математических наук, профессор, Киевский Национальный университет имени Тараса Шевченко, Украина, Киев-680, Академика Глушкова 2 корп. 6;
e-mail: firstname.lastname@example.org XII-th International Conference "Knowledge - Dialogue - Solution" BASIC STRUCTURE OF THE GENERAL INFORMATION THEORY Krassimir Markov, Krassimira Ivanova, Ilia Mitov Abstract: The basic structure of the General Information Theory (GIT) is presented in the paper. The main divisions of the GIT are outlined. Some new results are pointed.
Keywords: General Information Theory.
ACM Classification Keywords: A.1 Introductory and Survey Introduction There exist several common theoretical information paradigms in the Information Sciences. May be, the most popular is the approach based on the generalization of the Shannon's Information Theory [Shannon, 1949], [Lu, 1999]. Another approach is the attempt to be synthesized in a common structure the existing mathematical theories, which are applicable for explanation of the information phenomena [Cooman et al, 1995].
Besides of this, we need to point the diligence of the many researchers to give formal or not formal definitions of the concept "information". Unfortunately, although they are quite attractive in some cases, these definitions did not bring to any serious theoretical results [Abdeev, 1994], [Bangov, 1995], [Markov P., 2002], [Tomov, 1991], [Elstner, 1993].
At the end, there exist some works that claim for theoretical generality and aspire to be a new approach in the Information Science, but theirs authors should clear up what they really talk about [Burgin, 1997].
The theoretical base of the informatics needs the philosophical support and substantiation to become wide accepted scientific paradigm. This way, the closely scientific research in the domain of informatics would be able to leap across its boundaries and to become as elements of the scientific view of life.
Discovering the common philosophical base has exceptional importance.
The philosophical rationalizing and substantiating of the information phenomena become as leading goal of the scientific knowledge.
Starting point need to be the consideration that the General Information Theory (GIT) needs to be established as internal non-contradictory logical system of contentions [Markov et al, 1993]. This rule contrasts the understating of the informatics as a mosaic of formal theoretical works and applications.
Basic requirement is that the GIT needs to explain the already created particular theories and paradigms.
The mathematical structures ought to serve as a tool for achievement the precise clearness of the philosophical formulations and establishing the common information language for describing and interpreting the information phenomena and processes.
The second very important requirement is to build the GIT on the base of the inceptive philosophical definition of the concept "information" using as less as possible the primary undefined concepts with maximal degree of philosophical generalization. This requirement follows the consideration that the concept "information" is not mathematical concept. The behavior, peculiarity and so on could be described by the mathematical structures but this is another problem. In this case, the accent is stressed on the comprehension that the information has purely material determination and that it is a consequence of the interaction between the material objects as well as of the real processes and phenomena occurred in them and with them.
The presented in this paper General Information Theory (GIT) is based only on primary consideration of the world as variety of entities, which are formed by relationships between entities that form lower levels.
The development of GIT had started in the period 1977-1980. The first publication, which represents some elements of GIT, was published in 1984 [Markov, 1984]. The establishment of GIT was not rectilinear.
Occasionally, the influences of other paradigms have disturbed this process and have turned it to the vain effort [Burgin, Markov, 1991].
The fundamental notion of the GIT is the concept "Information". All other concepts are defined based on this definition. In 1988, the not formal definition of the concept of Information was published in [Markov, 1988].
20 Philosophy and Methodology of Informatics It became as a fundamental definition for the General Information Theory [Markov et al, 1993], [Markov et al, 2003a]. The translation of the philosophical theory into the formal one is a good approach for verification of the scientific ideas [Markov et al, 2003b], [Markov et al, 2004]. Because of this, the basic concepts of the General Information Theory ware presented philosophically and formally.
This paper is aimed to present the internal structure of GIT in its current state. For this purpose we will remember some main results as well as we will discuss the new achievements of GIT.
The GIT is build by three specialized theories:
Theory of Information, Theory of Infos, Theory of Inforaction.
Theory of Information The fundamental notion of the General Information Theory is the concept "Information". All other concepts are defined based on this definition. The first not formal definition of the concept of Information was published in [Markov, 1988]. The main philosophical explanations were published in [Markov et al, 1993]. Several attempts to develop a formal definition were introduced during the years [Markov et al, 2003b], [Markov et al, 2004].
Entity In our examination, we consider the real world as a space of entities. The entities are built by other entities, connected with relationships. The entities and relationships between them form the internal structure of the entity they build. To create the entity of a certain structural level of the world, it is necessary to have:
- the entities of the lower structural level;
- established forming relationship.
The entity can dialectically be considered as a relationship between its entities of all internal structural levels.
The forming relationship has a representative significance for the entity. The destruction of this essential relationship causes its disintegration. The establishment of forming relationship between already existing entities has a determine significance for the emerging of the new entity.
The forming relationship is the reason for the emergence of individual properties, which distinguish the new entity from the forming ones. The relationships form and present the entity.
Impact, Interaction, Reflection Building the relationship between the entities is a result of the contact among them. During the contact, one entity impacts on the other entity and vice versa. In some cases the opposite impact may not exist, but, in general, the contact may be considered as two mutually opposite impacts which occur in the same time.
The set of contacts between entities forms their interaction. The interaction is a specific interactive relationship between entities which take part in it.
The contacts of the given structural level are processes of interaction of the entities on the lower levels.
During the establishing of the contact, the impact of an entity changes temporally or permanently the internal structure of the impacted entity. In other words, the realization of the relationships between entities changes, temporary or permanently, their internal structure at one or at few levels.
The internal change in the entity, which is due to impact of the other entity we denote with the notion "direct reflection".
Every entity has its own level of sensibility. This means that the internal changes occur when the external influence is over the boundary of the sensibility of the entity.
The "reflection impulse" for given entity is the amount of the external influence needed for transition from one state to the reflection one.
The entities of the world interact continuously. It is possible, after one interaction may be realized another. In this case, the changes received by any entity, during the first interaction, may be reflected by the new entity.
This means the secondary (transitive external) reflection exists.
XII-th International Conference "Knowledge - Dialogue - Solution" The chain of the transitive reflections is not limited. In general, the concept “transitive impact” (respectively “transitive reflection”) of the first entity on the third entity through the second one will denote every chain of impacts (reflections) which start from first entity and ends in the third entity, and include the second entity in any internal place of the chain.
One special case is the external transitive self-reflection where the entity reflects its own relationships as a secondary reflection during any external interaction.
Some entities have an opportunity of internal self-reflection. The internal self-reflection is possible only for very high levels of organization of the entities, i.e. for entities with very large and complicated structure. The selfreflection (self-change) of the entity leads to the creating of new relationships and corresponding entities in it.
Of course, the internal self-reflection is a result of the interaction provided between entities in the lower levels of the structure of the entity. Such kind of entities has relatively free sub-entities with own behavior in the frame of self-preservation of the whole entity. As a result of the self-reflection, some relationships and corresponding subentities are created or changed in the entity.
The combination of the internal and external self-reflection is possible.
Finally let remark that the reflection could not be detected by the entity that contains it. This is dialectical behavior of the reflection - it is only an internal change caused by the interaction.
Information The real world contains unlimited number of entities. When an entity contacts another, there exists a great possibility to join third entity in this process. It is clear; the third entity may contact and reflect each of others as well as the process of realization of the interaction between them — the process of realization of the contact is a specific (temporal) forming relationship between entities and during the process of establishing the contact the entities form new (temporal) entity which in the same moment may be reflected by the third entity. So, the third entity may reflect any vestiges of this interaction from both first and second entities.
In the special case when the third entity contains reflections of the first entity received by both two different ways:
1. by transitive impact of the first entity on the third one through the second entity, 2. by impact of the first entity on the third one which is different from the transitive one, i.e. it can be direct impact or transitive impact through another entity (-ies) then the third entity became as an external relationship between first entity and its reflection in the second entity – it became as “reflection evidence” of this relationship.
- The first entity is called reflection source; the second entity is called reflection recipient; and the third entity is called reflection evidence.
In this special case, when there exist the triple "(source, recipient: evidence)", the reflection of the first entity in the second is called information in the second for the first entity.
Let point one very important case of the real world - simultaneous contacts of the three entities. Every one of them may be source, recipient and evidence in the same time. There exist six cases which represent the simultaneous contacts of three entities. Therefore, the entities A, B and C may be in the next six reflection relations: (A, B: C); (B, C: A); (C, A: B); (A, C: B); (C, B: A); (B, A: C).
All reflection relations are equivalent from point of view of the interrelations between reflection source, reflection recipient and reflection evidence. Because of this we will discuss only the case (A, B: C).
For practical needs, it is more convenient to follow the next consideration.
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