Symbolic Neutrosophic Theory
  Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract
symbols (i.e. the letters T, I, F, or their refined indexed letters Tj, Ik, Fl)
in neutrosophics. We extend the dialectical triad thesis-antithesis-synthesis
to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis. The
we introduce the neutrosophic system that is a quasi or (t,i,f) classical
system, in the sense that the neutrosophic system deals with quasi-terms
(concepts, attributes, etc.). Then the notions of Neutrosophic Axiom,
Neutrosophic Deducibility, Degree of Contradiction (Dissimilarity) of Two
Neutrosophic Axioms, etc. Afterwards a new type of structures, called (t, i, f)
Neutrosophic Structures, and we show particular cases of such structures in
geometry and in algebra. Also, a short history of the neutrosophic set,
neutrosophic numerical components and neutrosophic literal components,
neutrosophic numbers, etc. We construct examples of splitting the literal
indeterminacy (I) into literal subindeterminacies (I1, I2, and so on, Ir), and
to define a multiplication law of these literal subindeterminacies in order to
be able to build refined I neutrosophic algebraic structures. We define three
neutrosophic actions and their properties. We then introduce the prevalence
order on T,I,F with respect to a given neutrosophic operator. And the
refinement of neutrosophic entities A, neutA, and antiA. Then we extend the
classical logical operators to neutrosophic literal (symbolic) logical
operators and to refined literal (symbolic) logical operators, and we define
the refinement neutrosophic literal (symbolic) space. We introduce the
neutrosophic quadruple numbers (a+bT+cI+dF) and the refined neutrosophic
quadruple numbers. Then we define an absorbance law, based on a prevalence
order, in order to multiply the neutrosophic quadruple numbers.
