Multiplicative logic in arithmetic
Volodymyr Zhuravlov
TL;DR
This paper investigates the use of multiplicative logic in arithmetic as a model for many-valued projective logic, demonstrating that certain intervals form Heyting algebras and exploring their properties and generalizations.
Contribution
It introduces a novel framework linking multiplicative arithmetic to many-valued logic, identifying conditions for Heyting and Boolean algebra structures within this context.
Findings
Intervals form Heyting algebras under certain conditions
Conditions for Heyting algebras to be Boolean are identified
Numerical verification supports the theoretical claims
Abstract
The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be Boolean are identified. The article claims have undergone numerical verification. Paths for generalization to normed linear spaces are delineated.
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Taxonomy
TopicsMathematical and Theoretical Analysis · History and Theory of Mathematics