Modified Cognitive DIKWP Semantic Mathematics

Yucong Duan

International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com)

Abstract

This document presents a comprehensive proposal for a modified version of the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework, building upon previous investigations and incorporating Prof. Yucong Duan's critiques and revolutionary ideas. The modified framework addresses the paradox of traditional mathematics in AI semantics by prioritizing real-world semantics over abstract forms, integrating human cognitive processes, and constructing the framework in an evolutionary manner akin to infant cognitive development. Key enhancements include the explicit incorporation of human interaction in mathematical modeling, adherence to fundamental semantics, and the development of a Cognitive Semantic Space that evolves with the system's understanding. This proposal details the foundational principles, formal definitions, implementation strategies, and potential applications of the modified DIKWP Semantic Mathematics framework.

Artificial intelligence aims to emulate human cognitive abilities, including understanding, reasoning, and interacting with the world. Traditional mathematics has been instrumental in AI development but relies heavily on abstraction, often detaching mathematical constructs from real-world semantics. Prof. Yucong Duan identifies a paradox in this approach:

Paradox of Mathematics in AI Semantics: Traditional mathematics abstracts away from real semantics yet seeks to achieve semantic-rich AI understanding. This detachment hinders the development of genuine AI comprehension.

To resolve this paradox, Prof. Duan proposes a revolutionary approach:

1. Mathematics Should Conform to Basic Semantics: Instead of abstracting from semantics, mathematics should be grounded in them.

2. Inclusion of Human Cognitive Processes: Recognizing that mathematics is a product of human thought, human interaction and cognition should be integral to mathematical frameworks.

3. Prioritizing Semantics over Pure Forms: Semantics should have priority over the abstract forms used in traditional mathematics.

The modified DIKWP Semantic Mathematics framework aims to:

• Integrate Real-World Semantics: Ensure mathematical constructs are semantically meaningful and connected to the realities they represent.

• Incorporate Human Cognition: Model human cognitive processes explicitly within the mathematical framework.

• Construct an Evolutionary Cognitive Semantic Space: Develop a semantic space that evolves as the system's understanding grows, similar to infant cognitive development.

• Address Previous Limitations: Resolve paradoxes and limitations identified in prior versions, such as handling self-reference and undecidable statements.

The modified framework emphasizes three fundamental semantics:

• Sameness: Recognizing shared attributes or identities between entities.

• Difference: Identifying distinctions or disparities between entities.

• Completeness: Integrating attributes and relationships to form holistic concepts.

These semantics are not abstracted away but serve as the foundational building blocks of the mathematical constructs within the framework.

• Infant Cognitive Development Model: The framework evolves its semantic and conceptual spaces as an infant does, starting from basic perceptions and progressively developing complex understanding.

• Dynamic Growth: The cognitive semantic space expands as new semantics are learned and integrated, allowing the system to adapt and refine its understanding continuously.

• Explicit Modeling of Cognition: The framework includes representations of conscious and subconscious reasoning processes.

• Human Interaction: Recognizes the role of human interaction in shaping understanding and semantics, allowing for collaborative learning and knowledge sharing.

• Semantics First: Mathematical forms are developed to represent semantics accurately, not the other way around.

• Adherence to Realities: Ensures that mathematical constructs remain connected to the real-world phenomena they model.

• Sensory Inputs: The system starts with basic perceptions, analogous to an infant's sensory experiences.

• Primitive Semantics: Initial semantics are formed based on these perceptions, representing fundamental concepts.

• Concept Formation: Through interaction and experience, the system forms more complex concepts by combining primitive semantics.

• Semantic Relationships: Identifies relationships between concepts, such as causality, hierarchy, and association.

• Adaptive Mechanisms: The framework includes mechanisms for learning from new experiences, updating existing semantics, and forming new ones.

• Error Correction: Utilizes feedback to correct misunderstandings or incomplete semantics, refining the cognitive semantic space.

• Conscious Reasoning: Represents logical reasoning processes, decision-making, and problem-solving strategies.

• Subconscious Processing: Includes patterns recognition, intuition, and other subconscious cognitive functions.

• Communication Protocols: Establishes methods for the system to communicate with humans and other systems, sharing semantics and concepts.

• Shared Cognitive Development: By interacting with humans and other systems, the cognitive semantic spaces can align, reducing misunderstandings.

• Definition: A semantic bundle is a formal association of a concept with its evolved semantics.

• Structure: Includes the concept's attributes, relationships, context, and any relevant temporal or modal information.

• Concept: "Dog"

• Semantic Bundle:

• Attributes: Animal, four-legged, barks.

• Relationships: Pet of humans, member of the canine family.

• Contextual Information: Domestic vs. wild contexts.

• Temporal Information: Changes in the concept over time (e.g., breeds developed through domestication).

• Hierarchical Semantic Levels: Organizes semantics into levels to prevent paradoxes arising from self-reference.

• Level 0: Primitive semantics.

• Level 1: Concepts built from Level 0.

• Level 2: Meta-concepts about Level 1, and so on.

• Type Theory Integration: Assigns types to semantics to enforce rules and prevent invalid self-referential constructs.

• Acknowledgment of Incompleteness: Recognizes that certain statements may be undecidable within the system.

• External Reasoning Mechanisms: Allows for meta-system reasoning or human intervention to address undecidable statements.

• Evolutionary Adaptation: The system can evolve its semantics to incorporate new knowledge that resolves previously undecidable issues.

• Mathematical Forms as Representations: Forms are developed to accurately represent the underlying semantics, not as abstract entities detached from meaning.

• Semantic Integrity: Ensures that mathematical operations preserve the intended meanings of the concepts involved.

• Set Theory with Semantics:

• Traditional Approach: Abstract sets without inherent semantics.

• Modified Approach: Sets represent collections of semantically related entities, with operations reflecting meaningful relationships.

• Logic and Reasoning:

• Traditional Logic: Focuses on form without considering semantic content.

• Modified Logic: Incorporates semantic content into logical reasoning, ensuring conclusions are meaningful in context.

• Definition: A basic unit representing a concept, object, or idea, bundled with its evolved semantics.

• Notation: $E=⟨C,S⟩$, where $C$ is the concept and $S$ is the associated semantics.

• Definition: A connection between two or more semantic entities that represents a meaningful association.

• Types of Relationships: Hierarchical (e.g., subclass), associative (e.g., related concepts), causal, temporal.

• Nodes: Represent semantic entities.

• Edges: Represent semantic relationships.

• Contextual Layers: Different contexts are represented as layers or dimensions within the space.

• Growth: New nodes and edges are added as the system learns.

• Refinement: Existing semantics are updated or refined based on new information.

• Pruning: Irrelevant or incorrect semantics are removed.

• Operation: Combining primitive semantics to form new concepts.

• Rule: Ensures that the new concept's semantics are a coherent integration of the underlying semantics.

• Operation: Deriving new knowledge from existing semantics using logical reasoning.

• Rule: Inferences must preserve semantic integrity and be contextually valid.

• Operation: Adjusting semantics to align with those of other entities (e.g., during communication).

• Rule: Alignment seeks to minimize misunderstandings and ensure consistent interpretations.

• Machine Learning Techniques: Utilize algorithms that mimic human learning processes, such as reinforcement learning and unsupervised learning.

• Incremental Learning: The system learns progressively, integrating new semantics without requiring complete retraining.

• Natural Language Processing: Enables communication with humans to acquire new semantics and clarify existing ones.

• Feedback Mechanisms: Incorporates user feedback to correct and refine semantics.

• Graph Databases: Employ graph structures to represent the cognitive semantic space efficiently.

• Semantic Web Technologies: Utilize standards like RDF and OWL to encode semantics formally.

• Cognitive Architectures: Implement architectures that model human cognition, such as ACT-R or SOAR, adapted to incorporate DIKWP principles.

• Subconscious Processing Modules: Include components that handle pattern recognition and intuition, supporting conscious reasoning processes.

Scenario: The system encounters the concept of a "bicycle" for the first time.

Process:

1. Perception: Receives sensory inputs (images, descriptions) of a bicycle.

2. Semantic Formation:

• Sameness: Recognizes shared attributes across different bicycles (two wheels, pedals).

• Difference: Distinguishes bicycles from motorcycles (absence of engine).

• Completeness: Integrates attributes to form the holistic concept of a "bicycle."

3. Bundling: Creates a semantic bundle for "bicycle" with its associated semantics.

4. Integration: Incorporates "bicycle" into the cognitive semantic space, relating it to existing concepts (e.g., "vehicle," "transportation").

Scenario: The system communicates with a human who uses the term "bank" in a financial context.

Process:

1. Initial Interpretation: The system retrieves the semantics for "bank," which includes both financial institutions and riverbanks.

2. Contextual Analysis:

• Contextual Clues: Analyzes surrounding information to determine the correct context.

• Disambiguation: Selects the "financial institution" semantics based on context.

3. Semantic Alignment:

• Confirmation: May ask clarifying questions if uncertainty remains.

• Adjustment: Aligns its semantics with the human's usage to ensure accurate understanding.

4. Response Generation: Provides a contextually appropriate response, demonstrating comprehension.

• Contextual Comprehension: Handles ambiguous or context-dependent language effectively.

• Semantic Richness: Provides nuanced interpretations of language, capturing implied meanings.

• Shared Cognitive Development: Multiple AI systems develop semantics collaboratively, leading to consistent understanding.

• Distributed Learning: Systems share knowledge and experiences to accelerate learning.

• Natural Communication: Interacts with humans in a way that mirrors human conversation and understanding.

• Personalization: Adapts to individual users' semantics and communication styles.

• Complex Reasoning: Handles problems requiring deep understanding of semantics and context.

• Ethical Decision-Making: Incorporates values and purpose into reasoning processes, aligning with human ethics.

• Modular Design: The framework is designed to be scalable through modular components.

• Efficient Algorithms: Employs algorithms optimized for handling large semantic networks.

• Complementary Approaches: Uses traditional mathematical methods where appropriate but grounds them in semantics.

• Bridging Constructs: Develops constructs that translate between traditional abstract forms and semantically rich representations.

• Resource Management: Implements strategies to optimize resource usage, such as prioritizing critical semantics.

• Advancements in Hardware: Leverages modern computing technologies, including parallel processing and cloud computing.

The modified DIKWP Semantic Mathematics framework offers a revolutionary approach to mathematics in AI, addressing the paradox identified by Prof. Yucong Duan. By grounding mathematics in fundamental semantics, integrating human cognitive processes, and constructing the framework in an evolutionary manner, it aligns mathematical constructs with real-world understanding. This approach enhances AI systems' ability to comprehend and interact meaningfully with the world, paving the way for genuine artificial intelligence that mirrors human cognition.

• Implementation: Developing a working prototype to test the framework's viability and effectiveness.

• Evaluation: Assessing the system's performance in real-world scenarios and refining based on results.

• Expert Input: Engaging with experts in cognitive science, linguistics, philosophy, and AI to enhance the framework.

• User Studies: Conducting studies to understand how humans interact with the system and how it can be improved.

• Responsible AI: Ensuring the system's actions align with ethical standards and societal values.

• Transparency: Making the system's reasoning processes understandable to users.

1. Duan, 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 not 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. ".

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8. Russell, S., & Norvig, P. (2021). Artificial Intelligence: A Modern Approach (4th ed.). Pearson.

I extend sincere gratitude to Prof. Yucong Duan for his groundbreaking work on the DIKWP Semantic Mathematics framework and for inspiring this modified proposal. Appreciation is also given to researchers in cognitive science, artificial intelligence, philosophy, and related fields whose contributions have informed this work.

For further discussion on the modified DIKWP Semantic Mathematics framework and its applications, please contact [Author's Name] at [Contact Information].

Keywords: DIKWP Semantic Mathematics, Cognitive Semantic Space, Evolutionary Semantics, Human Cognition, AI Semantics, Prof. Yucong Duan, Mathematical Framework, Artificial Intelligence, Knowledge Representation, Cognitive Modeling