Day fifty -- Constructed linguistic universe (III)

      From Tienzen:
      Thus far, we have constructed two types of language, "type 0" and "type 1".
      Type 0 = {0, 0. 0. 0. 0. 0}
      Type 1 = {1, 1, 1, 1, 1, 1}
      Now, our question is that whether there is any "real" natural language having a similar structure to these two types of constructed language or not. Perhaps, some real natural languages are hybrids of these two.[/quote]

      The real natural language universe is very complicated. Yet, the constructed language universe is quite simple thus far, with only 8 definitions (including 3 operators) and 6 axioms. After introducing three more operators, its construction will be complete. Our final objective is to "derive" some languages which are similar with or identical to some natural languages. Yet, we should have a bird eyes view on this constructed language universe first. In fact, it has three layers (levels) of hierarchy.
         1. The pre-word layer (pw - sphere) -- this sphere is, in fact, not defined thus far in this constructed language universe. Yet, it will be the vital sphere for PreBabel. And, it will be added later.
         2. The word/sentence layer (ws - sphere) -- this sphere has three sub-layers
               1. the word sphere
               2. the phrase sphere
               3. the sentence sphere
            This ws-sphere is governed (or delineated) by two operators, "Operator" of composite (Opc) and "Operator" of dot (Opd).
         3. The post-sentence layer (ps - sphere) -- this sphere is context and culture laden or centered. In fact, the Sapir-Whorf hypothesis is defined in this sphere, and thus it is a major interest of our discussion. This ps-sphere is governed by the "Operator" of accumulation (Opa).

      Thus, each sphere is governed or delineated by operators. In this post, I will discuss only the ws-sphere. And, we can "derive" some theorems and laws now.

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

      By comparing with the English, what is the type of language for English in terms of this constructed language universe?
         1. English is inflected --> Ia = 1
         2. English has a "subject -- predicate" structure --> Pa = 1
         3. English has parts of speech, tense, numbers, etc. --> Ra =1
         4. English has word order --> Na =1

      For every real natural language, I think that it has Sa =1 and Ea =1. Thus, I will make this a law.

      Law one: For every real natural language, it has Sa = 1 and Ea =1.

      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}

      Now, we should be able to prove a theorem:
      Theorem 1: In comparing with the structure of English, a "type 1" language can encompass the English-like languages.

      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.

Signature --
PreBabel is the true universal language, it is available at