Day forty-seven -- A constructed linguistic universe (I)

      Tienzen wrote:
      These two approaches are dramatically different. Theory is always "hypothesis" centered. The constructed universe is built from the bottom up with some arbitrary definitions without any hypothesis.

      While the definitions for "word" and "sentence" are viewed as unsolved problems from the current linguistic theories, they can simply be defined as the building blocks for a "constructed linguistic universe". The followings are the definitions which demarcate the domain of a "constructed linguistic universe". Of course, this "constructed linguistic universe" will, then, be checked with the real linguistic universe, item by item.
         1. Definition one: Set UL = {Lx; Lx is a natural language}. So, the members of set UL are natural languages.
         2. Definition two: Set Vx = {syx; syx is a symbol in Lx}.
         3. Definition three: Wx is a "word" in Lx if and only if the following two conditions are met.
               1. Wx is a syx of Lx.
               2. Wx has the following attributes:
                     1. Wx has a unique topological form.
                     2. Wx carries, at least, one unique completed sound note.
                     3. Wx carries, at least, one unique meaning.

                  Note: In a universe, some terms are known intuitively and are not defined. In general, these terms are known via some other disciplines. The following terms are undefined.
                     1. Natural language
                     2. Set, member and symbol
                     3. topological form
                     4. Completed sound note
                     5. Meaning -- meaning is, in fact, a pointing function. When, F(wx) Arrow y, then, y is the meaning for wx.
         4. Definition four: "Operator" of composite (Opc) -- set Vx is the domain and the range for Opc. Opc (syx1, syx2, ...) = syxn Note: there can be some laws for Opc, such as, the Commutative, Associative, Distributive Laws.
         5. Definition five: "Operator" of dot (Opd) -- Opd is placed at the utmost right position of a syx. Opc cannot have any operand which carries an Opd.
         6. Definition six: Sx is a "sentence" in Lx if and only if the following two conditions are met.
               1. Sx must have, at least, two wx. That is, Sx = Opc (syxa, syxb, ...).
               2. Sx must be an operand of Opd. That is, Sx = Opd (Opc (syxa, syxb, ...)).
                  Note: Definition 6.a -- If Sx has only one wx, Sx = Opd (wx) is a "degenerated" sentence.
         7. Definition seven: Px is a "phrase" in Lx if and only if the following two conditions are met.
               1. Px must have, at least, two wx. Px = Opc (syxa, syxb, ...)
               2. Px must "not" be an operand of Opd.
         8. Definition eight: "Operator" of accumulation (Opa) -- Only "sentences" of Lx can be the operands of Opa. Opa stacks "sentences" of Lx into a linear chain.

      Seemingly these eight definitions are strange and simple. Can they truly demarcate a constructed linguistic universe? Can this constructed linguistic universe encompass the real linguistic universe? These are the issues that we must answer.

      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.

      For the "inflection axiom (IA)," there are two values for IA.
         1. IA = 0, the wx is not inflected.
         2. IA =1, the wx is inflected.

      Thus, two types of sub-domains (or languages) are created. By introducing, at least, three more axioms, the structure of different languages will emerge in details. I will use two real languages (English and Chinese) to check that how good this construction process is.

Signature --
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