An Arithmetization of Logical Oppositions

  • Fabien SchangEmail author
Part of the Studies in Universal Logic book series (SUL)


An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. To finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.


k-base system Bitstring Chasles’ relation Opposite Opposition Question-answer semantics Vectors 

Mathematics Subject Classification

Primary 03B35 Secondary 03B05 03B65 


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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