Stability, the ability to automatically extract and produce the efficient and accurate results of a defined problem without making epistemic assumptions, is discussed here as a possible memory system for understanding complex cognitive functions of the arithmetical learning. Stability is of top priority because it may typify organization of granule (knowledge-based information unit) structure. Memory efficiencies are that they depend on both linguistic factors and exposure to arithmetic training during granule formation or consolidation, supporting the idea of analog coding of numerical representations. Neuroimaging studies suggest that the parietal lobe as a potential substrate for a domain-specific representation of numeric quantities and associative memory mechanisms in stability, and results from these studies indicate that there may be the organization of number-related processes of stability in the parietal lobe. Stability seems to depend on the automatic information-processing system's response to experiential knowledge combining granularity (degree of detail or precision), maturational constraints, spatial factors (mental number line) and linguistic factors, making it an ideal candidate for understanding how these interactions play out in the cognitive arithmetic system.
The Formalization of The Arithmetic System on The Ground of The Atomic Logic