Space of notion. Detailed and curtailed form of presentation.

Notion – is an area of notion space, it could be determined as a number of atom features, each of them is a section on co-ordinate hub, measuring semantic space.

That’s is to say, notion could be presented as two vectors. The first of which is a number of co-ordinates of hyperflatness, reflected minimal co-ordinate value of this notion’s area bounds. The second is number of co-ordinate of hyperflatness, which limits maximum value of the same co-ordinates (“upper” hyperflatness).

N={N_min, N_max} or

N={N{x₁, x₂, …, x_n}, N{x_1’, x_2’, …, x_n’} or

N{{x₁, x_1’}, {x₂, x_2’}, …, |{x_n, x_n’}|}, N – is a n-dimensioned are in n-dimension space, nε∞, {1, …n} – are dimensions (co-ordinate hubs) of this space, x₁, x₂, …, x_n – are co-ordinates of lower hyperflatness’s area of space, x_1’, x_2’, …, x_n’ – are co-ordinates of upper hyperflatness’s area of space.

Expressions, presented earlier, determine detailed form of notion space presentation. However, practically most part of co-ordinates x_n=x_n’ (for objects), |x_n-x_n’ |ε0. that is to say, projection of concrete multi-dimension area to some dimension is nominal (that means, that this notion at this context hasn’t got a sense). Hence, for calculations and measuring this dimension for notion is considered to be degenerated, empty, curtailed. Co-ordinate data collated to this dimension considered to be zero in calculations. If this dimension is degenerated for the whole domain, it is clear, that those co-ordinates could be left out, noting in what domain calculations are held.

For enlarging approach could be said that totally notion space is a space with variable dimension. However, for each concrete area of semantic space, correlated to certain domain (object area), finite number of dimensions and its constancy could be accepted.

Thus, curtailed of estimated form of notion space presentation will be:

N={N_min, N_max} or

N={N{x₁, x₂, …, x_k}, N{x_1’, x_2’, …, x_k’} or

N{{x₁, x_1’}, {x₂, x_2’}, …, |{x_k, x_k’}|}, N – is a k-dimensioned are in n- dimension space, nε∞, k – is natural number, x₁, x₂, …, x_k – are co-ordinates of lower hyperflatness’s area of space, x_1’, x_2’, …, x_k’ – are co-ordinates of upper hyperflatness’s area of space.