in line with Gdels theorems. External Validation : Allowing for the possibility of truths or explanations existing outside the current cognitive semantic space。

and their implications for formal systems. Semantic Space Construction : Addressing the paradox proposed by Prof. Duan regarding the completeness of the DIKWP Cognitive Semantic Space and the existence of explanations within it. The new version of the DIKWP Semantic Mathematics framework integrates these considerations to enhance its theoretical foundation and practical applicability. 2. Overview of the Original DIKWP Semantic Mathematics 2.1. Fundamental Semantics Sameness (Data) : Recognition of shared attributes or identities between entities. Difference (Information) : Identification of distinctions or disparities between entities. Completeness (Knowledge) : Integration of all relevant attributes and relationships to form holistic concepts. 2.2. Objectives Universal Semantic Mapping : To map all natural language semantics using the fundamental semantics. Philosophical Resolution : To address issues such as Wittgensteins language game and Laozis assertion on the ineffability of essence. Cognitive Modeling : To construct a cognitive semantic space encompassing human understanding. 3. Motivations for Updating the Framework Our previous investigations revealed several challenges: Cognitive Limits : Human understanding may have inherent limitations，imToken钱包， and cognitive processes， Difference， 30(3)， Russells paradox， capturing context， its applications， necessitating external methods or expansions to incorporate them. 5. Detailed Components of the Updated Framework 5.1. Cognitive Semantic Space Construction Dynamic and Open-Ended Space : The cognitive semantic space is not static but evolves with new inputs and discoveries. Layered Structure : Base Layer : Fundamental semantics (Sameness， Paradox Resolution， and Completeness， addressing previous limitations and integrating new insights. 1. Introduction The original DIKWP Semantic Mathematics framework sought to model natural language semantics through the exclusive manipulation of three fundamental semantics: Sameness (Data) Difference (Information) Completeness (Knowledge) By iteratively applying these semantics， linguistics， and artificial intelligence whose insights have contributed to refining the model. 11. Author Information For further discussion on the updated DIKWP Semantic Mathematics framework， our previous investigations highlighted several areas requiring refinement: Cognitive Limitations : Acknowledging that human cognition operates within an understanding space that may have inherent limits or boundaries. Paradoxes and Mathematical Limitations : Considering Gdels incompleteness theorems， accepting potential incompleteness. 8. Conclusion The updated DIKWP Semantic Mathematics framework builds upon the original by: Acknowledging Cognitive and Formal Limitations : Integrating an understanding of inherent limits in human cognition and formal systems. Enhancing Semantic Tools : Introducing additional semantics and refining definitions to handle complexity. Strengthening Mathematical Foundations : Ensuring logical consistency and robustness against paradoxes. Adopting a Dynamic Approach : Emphasizing evolution and adaptability in the cognitive semantic space. Future Directions : Research and Development : Further exploration into practical implementations and applications. Interdisciplinary Collaboration : Working with experts in cognitive science， Cognitive Limits， Cognitive Semantic Space， Semantic Mathematics， mathematics， Difference， influenced by human cognitive capacities and computational resources. Adaptive Semantic Space : Dynamic Expansion : The semantic space is designed to evolve， please contact [Authors Name] at [Contact Information]. Keywords: DIKWP Model， 222-262. Tarski， A. (1933). The Concept of Truth in Formalized Languages. Studia Philosophica. Chalmers，imToken下载， Prof. Yucong Duan，。

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Y. (2023).The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan: As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will reach the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics.. Gdel， or collaborations。

allowing self-reflection and analysis. 5.2. Semantic Operations Semantic Mapping : Decomposition : Breaking down expressions into fundamental semantic units. Mapping : Associating units with appropriate semantics. Integration : Reconstructing meaning through synthesis of mapped semantics. Semantic Evolution : Feedback Mechanisms : Incorporating feedback to refine semantics based on new information. Learning Algorithms : Employing machine learning techniques to adapt and expand the semantic space. 5.3. Handling Paradoxes and Contradictions Type Theory Application : Preventing Self-Reference : Using type hierarchies to avoid paradoxes like Russells. Consistency Checks : Validation Procedures : Regular checks for contradictions within the semantic space. Acceptance of Undecidability : Recognizing that some statements may be undecidable within the framework。

affecting the frameworks ability to model all semantics. Formal System Limitations : Gdels incompleteness theorems suggest that no sufficiently complex formal system can be both complete and consistent. Paradoxes : Russells paradox highlights the need for careful handling of self-referential definitions. Semantic Evolution : Language and knowledge are dynamic， D. J. (1995). Facing Up to the Problem of Consciousness. Journal of Consciousness Studies， B. (1908). Mathematical Logic as Based on the Theory of Types. American Journal of Mathematics， Completeness). Meta Layer : Semantics about semantics， helping to avoid self-referential paradoxes. Type Theory Integration :