basic structures

down to [ α-structures | β-structures | γ-structures | other structures | (γ-β-α)-translation | β-equivalences ] – up to 2^2-structures or jump to the general structures


NOT.11.EmergenceLogicalCubeOppositional geometry (OG) is a new branch of mathematics made of “oppositional structures” and of transformations between them. The main structures of OG are the α-, β- and γ-structures. They are mutually related by a rule of OG-translation, which allows, for instance, to translate modal logic or generalised quantifiers or conceptual networks (expressed via γ-structures) into “oppositional hyper-geometry” (expressed via βn-structures). The α-structures and β-structures are made of “logical bi-simplexes of dimension m” The βn-structures yield a new notion of mathematical equivalence, the βn-equivalence (between γ-structures). For going from the theory of the oppositional bi-simplexes to the theory of the oppositional poly-simplexes go to the general structures.


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