Iconic and Dynamic Models to Represent “Distinctive” Predicates: The Octagonal Prism and the Complex Tetrahedron of Opposition

  • Ferdinando CavaliereEmail author
Part of the Studies in Universal Logic book series (SUL)


The predications of the Blanché Hexagon, enriched by converses and negative terms, can be integrated into the ‘Octagonal Prism’ of Opposition, an exhaustive model drawn from Distinctive Predicate Calculus, here presented in iconic version. The 7 basic expressions, added to 9 cases without any existential presuppositions, are exhaustive and geometrically organizable in a Complex Tetrahedron of Opposition. This model has ‘dynamic’ features and a substructure, the ‘Double Diamond’, that is semantically interpretable in terms of synonymies that are gradually different, and can play an important role in theoretical and applied disciplines (e.g.: semantic search engines, translators).


Distinctive logic Hexagon of opposition Knowledge representation Non-standard logic Predicate logic Synonymies Tetrahedron of opposition 

Mathematics Subject Classification

Primary 03B65 Secondary 68T30 03B20 03B22 03B60 03B80 


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Circolo Matematico CesenateCesenaItaly

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