# An Arithmetization of Logical Oppositions

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## Abstract

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.

## Keywords

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

## Mathematics Subject Classification

Primary 03B35 Secondary 03B05 03B65## References

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