Cell Theory Continuation of Quantum Theory for Language Projective Space as Scheme for Word Order

 Cell Theory

 

Continuation of Quantum Theory for Language

 

Projective Space as Scheme for Word Order

 

　　　TANAKA Akio

 

1 n-dimensional complex projective space Pⁿ is defined by the following.

Sch is category of scheme. Set is category of set. X is scheme.

Contravariant functor h_x : Sch → Set

h_x (S) = Hom_sch (S, X)

Pⁿ = h_x (Spec(C))

Pⁿ becomes scheme for expressing h_x.

2 P² that is defined by 2-dimensional homogeneous polynomial is presented.

Closed scheme of P², X = Proj C |x, y, z| becomes <line>, <circle> or <surface> by affine transformation.

<Surface> is projective manifold.

3 Weighted projective space that is projective algebraic manifold is defined by the following.

P (a₀, …, a_n) = Proj C |x₀, …, x_n|

4 Weight is identificated to word order of language.

5 Language is expressed by algebraic manifold, especially by projective scheme.

 

[Reference]

Cell Theory /  From Cell to Manifold / Tokyo June 2, 2007

Cell Theory / Conifold as Word / Tokyo June 9, 2007

 

Tokyo June 11, 2007

Sekinan Research Field of Language

www.sekinan.org