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Recursive Epistemic Mathematics: A Foundational Framework for Incompleteness-Aware Cognitive…
- The document proposes Recursive Epistemic Mathematics (REM) as a framework integrating Gödelian incompleteness, transimaginary probability, and chaotic-differential semantics into language modeling systems.
- REM defines cognition as the evolution within a Transimaginary Phase Space, modulated by non-linear differential equations and an internal Gödelian Operator.
- It addresses the limitations of current language models by handling probabilistic superposition, contextual drift, epistemic classification, and dynamical evolution.
- The framework includes mathematical structures like complex and dual numbers, arithmetic operations, and the Gödelian Operator for system incompleteness awareness.
- Token generation in REM involves a Selection Potential Function with probabilistic, dynamical, and epistemic fitness components.
- The recursive update dynamics in REM ensure convergence to fixed-point distributions while maintaining epistemic consistency.
- Theoretical properties of REM include epistemic completeness, semantic stability, and incompleteness awareness, distinguishing it from traditional systems.
- Implementation considerations for REM involve numerical integration, Gödelian Operator training, and hardware requirements for optimized performance.
- In conclusion, REM offers a rigorous foundation for cognitive architectures that acknowledge epistemic limitations, making strides in self-aware AI development.
- Future research directions should explore efficient implementation, empirical validation of the Gödelian operator, and emergent properties of incompleteness-aware systems.
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