[ p^q-semantics | p^q-lattices | n*p^q-parallelepiped | p^2-structures | p^3-structures | p^4-structures | p^5-structures | … | p^q-structures ] – down to the basic structures

Oppositional 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- and β-structures are made of “logical poly-simplexes of dimension *m*” (most of the time logical bi-simplexes of dimension *m*), generated by the Aristotelian p^q-semantics (and their Aristotelian p^q-lattices). The *βn*-structures yield a new notion of mathematical equivalence, the βn-equivalence (between γ-structures).

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