Day fifty-one -- Constructed linguistic universe (IV)

From Tienzen:
Thus, we can rewrite the language "type" equation, Lx (a real natural language) = {1, Pa, Ia, Ra, Na, 1}. Then,

Type 0 = {Pa, Ia, Ra, Na} = {0, 0, 0, 0}
Type 1 = {Pa, Ia, Ra, Na} = {1, 1, 1, 1}

... Corollary 1: English is a "type 1" language. Then, we can compare the other real natural languages with this constructed language universe, one by one. Yet, I think that two will be enough to prove the point, and I will make such a comparison with Chinese language in my next post.[/quote]

With the previous definitions:
Similarity transformation axiom -- Sa
Predicative axiom -- Pa
Inflection axiom -- Ia
Redundancy axiom -- Ra
Non-Communicative axiom -- Na
Exception axiom -- Ea

For Sa = 1, all other axioms are either repeating or inherited in each level or sub-level through out the hierarchy. Thus, the language "type" equation can be and should be written in better details, such as,

Lx (a real natural language) = word {Pa, Ia, Ra, Na} + phrase {Pa, Ia, Ra, Na} + sentence {Pa, Ia, Ra, Na}

For Chinese language,
Pa = 0 for all levels.
Ia = 0 for all levels.
Ra = 0 for all levels.

Yet, for Na (the Non-Communicative axiom), it is not a (0, 1) operator but is a fuzzy operator. And this fuzzy operator goes way beyond the coverage of Ea (Exception axiom).

For Chinese words, the Na basically equals to zero (0), but its exceptions go way beyond the Ea can cover. Thus, I must introduce a new concept, the "apostrophe", 0' is basically a 0 but with exceptions go way beyond the Ea can cover. Note: this case exists at the pre-word level which is not defined thus far.

For Chinese phrases, the Na basically equal to 1'; the word order of phrases does make difference most of the time.

For Chinese sentences, the Na basically equals to 0'; the word order of sentences does "not" make difference most of the time. Such as, (I love he) = (love he I) = (he I love) = (love I he)

Thus, Lx (Chinese language) = word {Pa, Ia, Ra, Na} + phrase {Pa, Ia, Ra, Na} + sentence {Pa, Ia, Ra, Na}
= word {0, 0, 0, 0'} + phrase {0, 0, 0, 1'} + sentence {0, 0, 0, 0'}

With such a complicated equation, we should introduce an arithmetics table to calculate it. As there are three parts, we can define the operation table as below,

0 + 0 + 1 = 0'
1 + 1 + 0 = 1'
0 + 0 + 0' = 0'
1 + 1 + 1' = 1'
0 + 0 + 0 = 0
1 + 1 + 1 = 1

and, 0' + 1' + 0' = 0', so,
Lx (Chinese language) = {Pa, Ia, Ra, Na} = {0, 0, 0, 0'} = 0'
That is, the Chinese language is a (type 0') language.

Now, we can re-visit the English language. Superficially, the English words are inflected at the "word form" level. Yet,
1. Many words can represent many distinct parts of speech.
2. The correct part of speech for many words cannot be decided without understanding the semantics or even the pragmatics of the context.

Thus, the Ia (inflection axiom) in English is not a perfect 1, and it should be 1'. That is, the English language should be a (type 1') language. Perhaps, the (type 0) and (type 1) are ideal languages.

Now, we know the difference between two languages. Is that difference superficial or fundamental? We need to introduce three more operators to answer this question.

Signature --
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