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# Introduction. Knowledge model

Co-ordinate theory of notion (semantic) space (CSNT) – is a section of information theory. Its aim is mathematic analysis of notions meaning. Notion (in this work) is a class, which including the same or sister objects of surrounding world, such as subjects, their conditions, properties and process. That’s why it is supposed to organize a systematization of notions in abstract multi-dimension space (notions’ space, semantic space further), where each notion corresponded to multi-dimension area in it. Further, should be investigated a mathematical apparatus of operations in this space (notion’s algebra) and studied its topology. For quantitative analysis it is supposed to normalize ‘notions – classes’ by their characteristics, ranging by hallmark for specific class.

Development of semantic space co-ordinate theory allows combining “qualitative” branch of information theory (semantics and linguistics) and “quantitative” branch (information theory created by **Viner, Shennon, Kholmogorov**).

Contemporary technology needs such model of information representing, which allows determine knowledge, stored in it, without human intellect or artifact algorithms (such as neural networks). It may not be out of place to draw a parallel with raster and vector ways of storing graphic images. That is to say, looking at content of raster image you can’t say unequivocally what the way of its construction is. On the other hand, the way of constructing of vector image is clear.

Such need conditioned by exponential increasing of information volume, saved in unsystemyzed way and characterized as “Internet – is a heap of garbage, and to find knowledge there is so hard, almost impossible”. That is to say almost all information stored by humanity represented in unstucturized “raster” format. But, at the same time, information, which is determined with their help, is seemed to look like catching by nets with cells 1 square meter size. It catch only the most common descriptions and rules. It is clear, that such concept gives too abstract models, and their application in real world is impossible without human intellect interfering.

Beside that, **abstract** and excessive summary of models don’t give a possibility to exchange algorithms and structures between different areas, transferring them from one area to another and using them. The reason is unobvious resembling of rules close in meaning in various fields of human activities because of different description languages, using absolutely different groups of notions in different areas.

Hence, it is necessary to find a way of knowledge’ description, which will be, in fact, “vector” format of information representing. It’ll let automatically systemize information without any human participation in a stale treatment process. That is the substance of the co-ordinate theory of notion (semantic) space

In other words, main idea is to use not only present model of knowledge’ description, based on associations, but also model, based on determination of exact position of notion in a certain co-ordinate system. Author shows, that for each notion, associated with an class of objects of surrounding world, exists a determination not only through association (“chair looks like sofa, but sofa is larger, it is possible to lie on sofa”), but also description as certain area of multi-dimension “notions’ space”. Hence, there is an ability of constructing unequivocal correspondence (reflecting) between a certain linguistic expression, describing certain object, property or action in surrounding reality, and area in multi-dimension notions’ space N(x_{1}, x_{2},…, x_{n}), X_{n} (n>∞) – are examples of co-ordinate hubs (**scales (extents)**) of this space. Author offer to call this scientific direction as “co-ordinate theory of notion (semantic) space ” Main stages of the theory are:

- Constructing a co-ordinate system for semantic (notion) space
- Constructing a map of semantic (notion) space
- Topology analysis of semantic (notion) space

It is necessary to note, that space of notions could be both objective (impersonal) and subjective. Let subjective semantic space be space of some individuals, and then objective (impersonal) semantic space is a result of collective agreement for reality description. This work at given period delineates and studies impersonal (objective) semantic space.

Also, it’s necessary to say, that words of human natural languages don’t equal to notions as object classes of surrounding world. Generally speaking, words of language are weakly linked with notions they determine. As rule, this link is also subjective, that’s to say each person perceives words and notions link individual (look “subjective semantic space”). Word is a code, determine the notion, moreover non-optimal (look 6.7. “compression and transmission of information from Co-ordinate theory of semantic space point of view”).

Then it is possible to construct a map of semantic space, describe sense relations and distance between real world notions through algebraic equations of “notion’s algebra”, “semantic algebra”, based on vector algebra and further studying of semantic space topology.

At the present time, another concept predominating. It uses different stretch surrogates of distance called “semantic links”, “weight coefficients” etc, reflecting, as usual, hierarchic and network correlation between terms, corrected by ajustment on destrotion altered by concrete natural languages. “Consanguinity”, “distance” in that contexts, in general, are immeasurable values. They give ability to numerical measuring of distance between conceptually close things (black and white, warm and cold). And how far notions “black” and “cold” are? Is this distance longer, then distance between “rough” and “blue”? Chair and bottle or computer and cup - what things are conceptually close to each other?

Co-ordinate approaching is a broadening of present approaches in describing space of notion - hierarchical and relative models. Thus, idea of notions’ space doesn’t cancel hierarchical, constructive and other correlations in no case, but adds them, making them measurable. For example, you can describe the position of leave on the tree for a long time, moving from trunk to branches. But it’ll be easier to find, if you initialize absolute polar co-ordinates: vertical and horizontal dimension, vector length from hub line of the trunk at the bottom. We’ll get only 3 numbers instead of large description of our way along the tree.

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