Difference， and the exploration of cognitive semantic spaces. The new version aims to provide a comprehensive and robust model for understanding and representing semantics， Formal Semantics https://blog.sciencenet.cn/blog-3429562-1453465.html 上一篇：Cognitive DIKWP Semantic Mathematics（初学者版） 下一篇：Modal DIKWP Semantic Mathematics（初学者版） ， this updated framework incorporates insights from cognitive development， 30(3)。

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then any understandable problems explanation is inherently accessible. 4. The New Version of DIKWP Semantic Mathematics 4.1. Incorporation of Previous Insights The new version integrates insights from previous investigations to enhance the framework: Acknowledging Cognitive Limits : Recognizes the inherent limitations of human cognition and formal systems. Refining Fundamental Semantics : Expands and clarifies the definitions of Sameness， representing the full set of attributes that define entity aa a in relation to others. Contextuality ( XX X ) : A function X(a)X(a) X ( a ) that maps an entity aa a to its contextual parameters. Hierarchy ( HH H ) : A mapping H(a)H(a) H ( a ) that assigns entity aa a to a level within a hierarchical structure. Temporal Dynamics ( TT T ) : A function T(a， providing tools to better understand and model complex semantic phenomena. References Duan， cognitive science， refining its theoretical underpinnings and extending its capabilities. It addresses previous limitations， Prof. Yucong Duan，b)C(a) = S(a， acknowledging that meanings can evolve over time. 4.2.2. Formal Definitions Sameness ( SS S ) : Defined as a relation S(a， t ) that describes the attributes of entity aa a at time tt t . 4.3. Addressing Limitations and Challenges 4.3.1. Cognitive Limits Scalability : The framework incorporates computational models to handle complex semantics at scale. Adaptive Learning : Emphasizes iterative refinement and learning mechanisms that mimic human cognitive development. 4.3.2. Paradoxes and Contradictions Type Theory Integration : Utilizes type hierarchies to prevent self-referential paradoxes. Axiomatic Constraints : Adopts axioms from formal logic and set theory to ensure consistency. 4.4. Formal Mathematical Framework The new version establishes a formal mathematical foundation: Set Theory Foundations : Based on axiomatic set theory (e.g.， cognitive science， mapping natural language semantics， Zermelo-Fraenkel with Choice) to avoid paradoxes. Logic and Proof Systems : Incorporates formal logic systems to enable rigorous proofs and reasoning.