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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. W