1 Sentence of language is expressed by plane or torus.
2 Torus is regarded topologically same as plane of Hilbert space.
3 Torus is a closed space.
4 On thinking about function space in torus space, infinite parallel translation can not be done for its closed space condition.
5 From viewpoint of quantum mechanics, torus is limited to discrete parallel translation for periodic condition of wave function.
6 Word of language is expressed by lineation of plane or torus.
7 Lineation consists of quanta that are entangled conditions.
8 Quantum and quanta carry semantic information on language.
9 What quantum becomes element of language is called quantum language. The abbreviation is QL.
10 Quantum language has discrete parallel translation on torus.
11 Quantum language breaks continuous symmetry.
12 Quantum language has discrete symmetry.
13 Quantum language clearly shows the spatial structure on language.
14 Language that consists of substantiality, abbreviated to SL, is topologically same between plane and torus, but is not symmetrically same between the two.
15 Breaking spatial symmetry on torus from plane indicates the existence of language’s classification.
16 Substantial language classifies two. One has continuous symmetry. The other has discrete symmetry.
17 Language has hierarchy that contains continuity at underlayer and discreteness at upperlayer.
18 Hierarchy of language is useful to semantic analysis. For instance, notion that contains truth-fault value is analyzed from hierarchy of language in which truth is treated to give continuity and discreteness but fault is treated to give only discreteness.
19 One assumption is now adopted that natural language has no layer and super-language containing truth-fault value and so forth has layer.
20 Natural language is finally contained to substantial language for the latter’s comprehensiveness.
21 Quantum language that has be clearly recognized the spatial structure will advance the research of language one step profoundly.
Tokyo June 11, 2006
Sekinan Research Field of Language
www.sekinan.org
Sekinan Research Field of Language
www.sekinan.org
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