Non-negative Rational Semantic Numeration Systems
This is a foundational theoretical contribution for researchers in numeration systems and dynamical systems, but it is highly abstract and lacks concrete applications or benchmarks.
The paper introduces positive rational Semantic Numeration Systems, defining carry and remainder operations for cardinal semantic operators, and explores their dynamical properties. It also proposes a first definition of partial integer Semantic Numeration Systems.
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.