Arithmetic Geometry Language
TANAKA Akio
[DRAFT]
Language, Word, Distance, Meaning and Meaning Minimum
by Riemann-Roch Formula
1
Finite generated Z module M
Positive Definite Hermitian form of M < , > : M × M → C
Hermitian Z module (M, < , >)
M's volume on < , > vol (M, < , >) = exp(-
(M, < , >))
(M, < , >))
M free Z module.
Free basis of M e1, ..., er
vol (M, < , >) = 
2
Reduced integer ring R
Total quotient ring of R K
Z free basis of R {w1, ..., wn}
DR:= det(TrK/Q (wi ・wj))
3
(Proposition)
vol(R, < , >
hcan = 
hcan =
4
Hermitian R module (H, h)
5
(Theorem)
Order r
Hermitian R module (H, h)
6
Metric of V 
7
Impression
Language := (H, h)
Word := 
Distance := hV
Meaning := V
Meaning minimum := H
[Reference]
Cell Theory / Continuation of Quantum Theory for Language / From Cell to Manifold /
June 2, 2007
Tokyo August 15, 2009
Sekinan Research Field of Language
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