Non-negative Rational Semantic Numeration Systems
2026-04-30 • Logic in Computer Science
Logic in Computer Science
AI summaryⓘ
The authors introduce a new type of system called positive rational Semantic Numeration Systems, which help represent numbers in a logical way using positive fractions. They explain how values called carries and remainders behave differently in these systems when using special semantic operators. The authors also study these systems as dynamic processes, showing how they change over time using math and computer examples. Finally, they make an initial step toward defining systems that work with partial integers.
Semantic Numeration SystemsPositive Rational NumbersCardinal OperatorsCarryRemaindersDynamical SystemsNumerationPartial IntegersAnalytical ExamplesNumerical Examples
Authors
Alexander Chunikhin
Abstract
A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The properties of positive rational Semantic Numeration Systems as dynamical systems are formulated and illustrated through analytical and numerical examples. A first attempt at defining partial integer Semantic Numeration Systems is proposed.