Algebraic Linguistics Linguistic Result Deep Fissure between Word and Sentence

Linguistic Result

Deep Fissure between Word and Sentence

　　  TANAKA Akio

Now language has some algebraic postulations below.

Word consists of elements R₁. The element has proto-meaning.

Word’s meaning is generated by product(・) of the elements.

The product of elements is called primary meaning (R₁, ・).

Word is group.

Another word ( R₂, ・)is generated.

New word is generated by addition (＋) of the elements of two words.

The addition of elements is called secondary meaning (R₁, R₂, ・, + ).

New word is ring.

The upper group and ring are regarded as commutative.

Sentence consists of words T₁.

Sentence is generated by product of words (T₁, ・).

But sentence is seemed to be non-commutative, i.e.T₁T₂T₃ is not T₃T₂T₁. /I/ /read/ /book/ is not /book/ /read/ /I/. Word is expressed by / /.

I call the situation <deep fissure between word and sentence>.

This <fissure> is seemed to be relative with true-false argument of sentences.

Tokyo September 10, 2007

Sekinan Research Field of Language

www.sekinan.org

Postscript January 21, 2008

[Basis]

<On differential structure between word and sentence>

Algebraic Linguistics / Linguistic Note / 12 / Coset / Tokyo August 6, 2007

[Foresight from past work]

<On true-false value>

Tube-Ring Theory / True and False Hierarchy of Language / For CHINO Eiichi and Prague / Tokyo July 25-28, 2006

Algebraic Linguistics / Linguistic Result / From Cut and Glue Dimension to Krull Dimension / 8^th for KARCEVSKIJ Sergej / Tokyo September 26, 2007

Postscript February 10, 2008

[Conjecture]

<On finiteness and Infinity on language>

Kac-Moody Lie Algebra / Finiteness in Infinity on Language / Tokyo February 10, 2008

Postscript August 2, 2008

[Conjecture]

<On Definition of word and sentence>

Stochastic Meaning Theory / Conjecture 1 / Tokyo July 12, 2008

<On warp and entropy of language>

Stochastic Meaning Theory / Conjecture 2 / Warp and Entropy / Tokyo July 25, 2008