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Day fifty-five -- Summary of constructed linguistic universe

      [quote from sangi39] The formatting of this forum leaves the long list of "equations" provided across the last 2-3 pages disjointed to the point where some don't make all that much sense. [/quote]
            I will organize these posts into a single page during the holiday. Now, I am briefly summarizing them as below.
               1. The objective -- instead of analyzing the "real" linguistic universe which is very complicated with many chaotic data sets, I am simply constructing a "constructed linguistic universe" with some arbitrary selected definitions, axioms, postulates, etc.. Then, I will compare these two universes item by item. If I can show that the "constructed linguistic universe" does encompass the "real" linguistic universe, then a "Super Unified Linguistic Theory" is constructed.
               2. The constructed linguistic universe --
                     1. Five definitions:
                           1. Definition one -- the set UL, it encompasses "all" languages, Lx, Ly, ....
                           2. Definition two -- the set Vx, it encompasses all symbols of "one" language, Lx.
                           3. Definition three -- the words
                           4. Definition four -- the phrases
                           5. Definition five -- the sentences
                        These five definitions demarcate a linguistic universe.
                     2. Three operators --
                           1. Operator of composite
                           2. Operator of dot (completion)
                           3. Operator of accumulations
                        These three operators delineate a three layer (sphere) hierarchy.
                           1. the Pre-word sphere
                           2. the word/sentence sphere
                           3. the post-sentence sphere
                     3. Six axioms --
                           1. Similarity transformation axiom -- Sa
                           2. Predicative axiom -- Pa
                           3. Inflection axiom -- Ia
                           4. Redundancy axiom -- Ra
                           5. Non-Communicative axiom -- Na
                           6. Exception axiom -- Ea
                        These six axioms identify the language type, "type 0" and "type 1". Then, can this great divide between these two types be bridged over?
                     4. Introducing the concept of "apostrophe," the type degeneration or deviation.
                     5. Two more operator:
                           1. Operator of pidginning
                           2. Operator of creoling
                        Two postulates:
                           1. Postulate one -- the "Operator of pidginning" transforms a language Lx toward the direction to the "type 0" language.
                           2. Postulate two -- the "Operator of creoling" transforms a pidgin (Lx) toward the direction to the "type 1" language.
                        Two predications:
                           1. Predication one -- the difference of the language structure in terms of "language type" between two pidgins is smaller than the difference between two original languages
                           2. Predication two -- The difference of the language structure in terms of "language type" between two creoles is smaller than the difference between it and its parent language.
                     6. One more definition and two more postulates
                        Definition on functionally equal
                        Postulate three: the major known natural languages, at least the Big 6, are functionally equal in the ws-sphere.
                        Postulate four: the Transitive Property holds for the (=F=), the functional equal.
               3. Conclusion and comparison:
                     1. Hypothesis one -- this "constructed linguistic universe" forms a linear language spectrum, ranging from the "type 0" to the "type 1". That is, all natural languages are distributed in this language spectrum, and this "constructed linguistic universe" encompasses the entire "real" linguistic universe.
                     2. Theorems -- all theorems of this "constructed linguistic universe" are applied on the "real" linguistic universe and to see whether they hold or not.
                           1. Theorem 1: English is a "type 1" language.
                           2. Theorem three -- the syntax sets of two natural languages are functionally equal.
                                    Corollary 3.1 -- Any two natural languages (Lx and Ly) are mutually translatable.
                           3. Theorem 4 -- the word sets of two natural languages are functionally equal.
                                    Corollary 4.1 -- Wx (Chinese) has only about 60,000 characters and Wy (English) has about one million words. Yet, Wx (Chinese) is functionally equal to Wy (English).
                     3. Hypothesis two -- the PreBabel principle.
            This outlines the entire framework for the "Super Unified Linguistic Theory."

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