Day forty-nine -- Construced linguistic universe (II)

      From Tienzen:
      After the demarcation of a domain, we, now, can and need to construct the internal structure of this domain. That is, we need to introduce some axioms now. With different axioms, the internal structure of the domain will be different or that different sub-domains will be constructed.

      Indeed, the definitions demarcate a domain; the axioms will specify the internal structure of that domain or to construct some sub-domains. I will "introduce" (arbitrary chosen) six axioms for this "constructed linguistic universe." Similarly to the Parallel axioms in Geometry, every axiom can have more than one value.
         1. Similarity transformation axiom -- a rule (theorem or law) will repeat over and over in a domain or in different levels of its hierarchy. And, it has two values;
               1. Sa = 0, similarity transformation is not active.
               2. Sa = 1, similarity transformation is active.
         2. Predicative axiom -- particles in a glob (a word, a phrase or a sentence) is distinguishable. And, it has two values;
               1. Pa = 0, PA is not active.
               2. Pa = 1, PA is active.

            When Pa = 1, a sentence "could" be first distinguished as the "Speaker" and the "others." If Sa = 1 also, then, the "others" can be further distinguished as,
               1. action (or state) words
               2. object (things or person) words
               3. pointing words, and these can be further distinguished as,
                     1. pointing the action words
                     2. pointing the object words
               4. gluing words
               5. others
         3. Inflection axiom -- some tags are tagged at the end of words. And, it has two values;
               1. Ia = 0, IA is not active
               2. Ia = 1, IA is active
                  Note: As I mentioned before, with some definitions and axioms, we can often find some theorems and/or laws. Now, we can identify a theorem.
                  Inflection theorem -- Lx is a natural language. If Pa = 1 and Sa = 1 for Lx, then Ia =1 for Lx.
         4. Redundancy axiom -- For a function F, it will be applied, at least, twice on a particle. And, it has two values;
               1. Ra = 0, RA is not active
               2. Ra =1, RA is active
               1. Ra = 0;
                  I go to school "yesterday".
                  I have "three" dog.
                  I love He.
                  She love I.
               2. Ra = 1;
                  I "went" to school yesterday.
                  I have three "dogs".
                  I love him.
                  She loves me.
         5. Non-Communicative axiom -- for (a, b) and (b, a), they are "not" the same. And, it has two values;
               1. Na = 0, NA is not active
               2. Na = 1, NA is active
            For a sentence,
               1. when Na = 0,
                  (I love you) = (love you I)
                  Note: If a Lx has Na = 0, it will run into some problems, such as, Is (I love you) and (You love I) the same? Yet, there are some ways to resolve this kind of issue, and I will discuss it later.
               2. when Na = 1, then the "word order" is a rule.
         6. Exception axiom -- for every rule in the universe, there is one or some exceptions. And, it has two values;
               1. Ea = 0, EA is not active
               2. Ea = 1, EA is active

      With these six axioms, a constructed language can be expressed as,
      Lx (a constructed language) = {Sa, Pa, Ia, Ra, Na, Ea}

      And, 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. This will be our future discussion.

      My hope is that all real natural languages will fall in-between these two types.

Signature --
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