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Main principles of co-ordinate semantic space theory (space of notions)

Main principles of co-ordinate semantic space theory (space of notions)

Main definitions

This work uses followed definitions:

Notion area of abstract multi-dimension space of notion (subspace), adequate to some class of objects in real world

Each class could have subclasses. Each class could have some ancestor-classes. Hence, each class-descendant:

Has inherited features, which characterize its rating to ancestor-class

Could have additional feature (property, characteristics), differ this class form another (look Hypothesis of incremenation, 7.3.)

Class (domain) group of objects, which has same features, significant to rank object among this class (for detecting objects as class representatives).

For example, class chair implies an object for sitting with back, without elbow-holders. Thus, features with back and without elbow-holders are significant for ranking object among class chair. Whereas features color, material, and even number of legs are insignificant.

Example. Notion kitchen furniture is a descendant (as minimum) of class furniture with additional feature using on kitchen. Notion kitchen chair is a descendant (as minimum) of classes kitchen furniture and chairs. Notion blue kitchen chair adequate to kitchen chair class with additional feature blue.

Feature is also a class (notion) and could be presented as number of ancestor-classes. If ancestor of class of that feature is some amount of monosemanticaly ranged notions, sorting of which could be presented as number series sections with imprecise edges, as rule, so this feature is an atom (protofeature, basic feature) and dimension of notion space.

For example, feature color could has subclass blue, green, red, lilac, scarlet etc). Each subclass could be presented as couple of atom features length of wave and intensity of eradiation. Sorting by atom features defines mutual position of classes in notion space.

Thus, notion space (semantic space) is abstract space, which consists of mono-dimension spaces, and each mono-dimension space divided into pieces, containing definite atom feature (property, characteristic) of notion class.

It is supposed, that while describing concrete class we couldnt fined some concrete feature (for example, chair doesnt have power), than this feature became zero (rolled up) mono-dimension space, but still take into consideration in calculations (not to be ignored).

All objects-things involved in some process. Each class (area in semantic space) linked with one or several functions, which define in what process could be (take part, locate) this subject as representative of this class. Process changes features-properties of some definite object-subject. Thus, number of important objects feature depends on in what process could object take part (that is to say, his functions).

From the point of view of notion space there is no principal difference between classes of objects, which traditionally divided in languages on nouns, verbs, adjectives. Object-class present object (noun), process (verb) or feature (adjective or adverb). It allows holicistically approach to reality describing notion-class contains object-action-feature.

Process is (in this work) a vector of abstract force, which changes features (that is to say, co-ordinates) of subjects, that is to say move object inside notion space. Analogously to notions and features, there is also a hierarchic structure of classes for processes. Process, that changes only one atom feature supposed to be atom process.

Thus, approaching to describing notion space from processes author could say, that condition of subject in number of processes determine current position of subject-object in notion space and its current rating.

Atom process activate or deactivate one feature, thats why this process could be identified to this feature, correlated to some function, that is to say, to come from vector presenting to function. Each process could be divided into number of atom process by superposition. Function of subject also could be presented as number of vectors of atom processes. Thus, for object to acquire necessary functions (acquire identity to necessary classes) and appear in proper area of notion space some atom processes with its components should be carried out, superposition of them gives necessary function.

Module of this vector-function supposed to call semantic force of process. This value describes a volume of information, transferred to the object at its creating.

Class (domain) is named multi-dimension area (subspace) in notion space, which combine notions in groups by hierarchical features (notion chair in domain furniture or knife in domain kitchen appliance). Hierarchic relations between notions regulated by domain. Domains have internal structure of notion space. In fact, they are cross-section of notion space by definite features.

From those consideration it is clear, that object is universal structure, thus subjects, actions, modificators are object presentations (projections). Author has to note that compares with natural languages hold up as an example are not analogues at all, and used only for convenient.

Subject is object of class as certain condition, which in natural languages determined as noun (run, construction);

Action is an object of class as certain process, which in natural languages determined as verb (to run, to build). As process it could change the essence of the object and move it to another area of semantic space in another class.

Subject modificator is an object of class as changing of condition, which doesnt change the essence of the object (move it to semantic space within the its class limits). In natural languages it is described as adjective or participle (running, building).

Action corrector is an object of class as certain changing of process, whih doesnt change the essence of process (moving it to semantic space within its class limits). In natural languages is described as adverb.

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