Semantic Evolution and Self-Feedback Mechanism under the DIKWP S

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Semantic Evolution and Self-Feedback Mechanism under the DIKWP S

通用人工智能AGI测评DIKWP实验室

2025-11-10

Semantic Evolution and Self-Feedback Mechanism under the DIKWPSemantic Mathematics Framework

Yucong Duan

Benefactor: Shiming Gong

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

The DIKWP Semantic Mathematical Framework decomposes the cognitive process into five levels: Data, Information, Knowledge, Wisdom, and Purpose. It strictly defines the transformation and interaction mechanisms between each level through semantic mathematical forms. First, starting from the three fundamental semantic elements of semantic mathematics—Sameness, Difference, and Completeness—we construct the evolution function models such as data information (), information knowledge (), knowledge wisdom (), and wisdom purpose (). These models depict how semantic content is generated and enriched layer by layer in the semantic space until high-level semantics (such as wisdom semantics and purpose semantics) emerge. Second, based on the network model of DIKWP, we systematically classify the important self-feedback paths between each level and reveal their interaction mechanisms and temporal rhythms in the form of feedback matrices and cyclic diagrams. The analysis shows that the combination of different feedback paths has a structural impact on the semantic system: some closed-loop feedbacks maintain system stability and balance, while others can stimulate the emergence of new semantics or drive the continuous evolution of the system’s purpose. Third, we refer to the meta-analysis results of neuroscience on consciousness and self in the past five years, which reflect the rationality of the DIKWP semantic mechanism from a physical level. For example, phenomena such as the P300 component in electroencephalography, spontaneous activity of the default mode network (DMN), and whole-brain gamma synchronization can be regarded as the neural counterparts of semantic difference confirmation, wisdom integration, and top-down feedback processes in the DIKWP model. This kind of refractive analysis emphasizes that we do not use neural mechanisms as the basis for modeling, but rather verify and inspire the improvement of the semantic mathematical model through these physiological evidences.Conclusion: The DIKWP Semantic Mathematical Framework provides a unified description of semantic evolution and feedback in the cognitive process. Without relying on the assumptions of existing neuroscience or consciousness theories, we use deductive reasoning to strictly define the mechanisms of semantic generation and self-feedback, and enhance the model’s explainability and credibility through the refractive analogy of neuroscience findings. This research lays a semantic mathematical foundation for the construction of explainable artificial consciousness systems, and the illustrative model diagrams are conducive to subsequent algorithm implementation and system development.

1Introduction

In the fields of artificial intelligence and cognitive science, formalizing the semantic understanding process has always been one of the core challenges. The traditional DIKW model describes the process from raw data to wise decision-making in the form of a hierarchical pyramid, but its linear and static structure is difficult to fully reveal the subjective purpose-driven and dynamic feedback roles in the cognitive process. In particular, when we try to endow machines with human-like consciousness and understanding, relying solely on bottom-up data accumulation is far from enough. On the contrary, human cognition is often purpose-oriented, with expectations and assumptions, and constantly corrected in the process. This suggests that we need a model that can reflect top-down purpose regulation and closed-loop interaction.

The DIKWP Semantic Mathematical Framework proposed by Professor Yucong Duan was born to solve the above shortcomings. DIKWP is an abbreviation for “Data-Information-Knowledge-Wisdom-Purpose”, which is a network model of five semantic levels: Data, Information, Knowledge, Wisdom, and Purpose. This model has two key innovations: First, it introduces “Purpose” as the highest-level semantic element, emphasizing that the cognitive process ultimately serves a specific purpose; Second, it breaks the linear hierarchical constraints and changes to a networked multi-directional interaction, forming a closed loop between the five elements. In other words, in the DIKWP model, the levels are not isolated and advanced step by step, but interact with each other through rich feedback paths to form an organic whole. For example, in practice, we often have intentions and decisions at play before collecting data, as research points out: “There is already a purpose at play before collecting data”. This view is structurally reflected in the DIKWP model, that is, the highest-level purpose (P) can affect the acquisition and selection of the lowest-level data (D), running through the entire process.

Semantic mathematics provides a rigorous formalization basis for the DIKWP model. According to Professor Yucong Duan’s theory, the semantics of all things in the world can be reduced to three basic elements: “Sameness”, “Difference”, and “Completeness”. These three elements are the cornerstones for constructing all complex semantics. By combining the three elements of “Sameness, Difference, and Completeness”, any natural language semantics can be mapped and formally described. For example, “Sameness” corresponds to identifying the consistency or similarity in semantics between two things, “Difference” corresponds to distinguishing semantic differences, and “Completeness” corresponds to establishing a complete concept, integrating related semantic units into a whole. The DIKWP framework is based on these three basic semantics as axioms to construct the expression and transformation of the five-level semantics in mathematics.

After this introduction, this paper will be divided into three main parts. The first is semantic evolution modeling: The mechanism of semantic generation from data to information, to knowledge, to wisdom, and then to purpose is derived in detail, clarifying the “Sameness-Difference-Completeness” semantic elements relied upon at each step of transformation, and giving formalized functional model representations (, , , ). The second is feedback path modeling and diagram: Based on the DIKWP network model, 25 possible level interactions (55) are identified and classified, and the important feedback paths are represented in the form of matrices and topological diagrams. The impact of these feedbacks on the dynamics of the semantic system under different combinations is analyzed, including the formation of stable closed loops, the stimulation of semantic emergence, and the continuity of purpose-oriented evolution. The third is neural refractive verification: We select several empirical results in consciousness and cognitive neuroscience (such as P300 brain waves, the function of the default mode network DMN, gamma band synchronization, etc.), and regard them as physical “refractive mirrors”, mapping back to the semantic processes of the DIKWP model to illustrate that the DIKWP framework can explain and unify these observed brain phenomena to a certain extent. Of course, this kind of refractive analysis is one-way. We do not correct the semantic model in reverse based on neural facts, but use it as an auxiliary means to verify the rationality of the model. Finally, the main findings of this study are summarized, emphasizing the significance of the DIKWP Semantic Mathematical Framework in the design of artificial consciousness systems and looking forward to future work.

2Evolution Path of Semantic Generation Mechanism

In the DIKWP Semantic Mathematical Framework, each level (D/I/K/W/P) has its specific semantic definition and function. More importantly, adjacent levels are connected through functional semantic transformations. According to Professor Yucong Duan’s theory, these transformations correspond to the application and combination of the semantic basic elements “Sameness, Difference, Completeness”, thereby realizing the evolution of semantic content between different levels of abstraction. Below we analyze the mechanisms of each transformation in turn according to the levels and give formalized models.

Data (Data): As the atomic level of cognition, the data level mainly carries the semantics of sameness, that is, it focuses on the patterns and signals in objective facts that can be identified as the same or repeatedly appearing. Data is usually raw symbols or perceptual inputs that have not been interpreted, with limited but stable semantic connotations. The manifestation of sameness semantics in the data layer is: if raw records from different sources are the same in some key features, we classify them into the same category or consider them to express the same concept. For example, in medical practice, if the symptom data of different patients shows high similarity (“Sameness”), it can be summarized as the same clinical manifestation. The “Sameness” semantics of the data layer lays the foundation for subsequent information interpretation and wise decision-making. Formally speaking, data D can be represented as a set or vector of observations, and the semantic extraction function of the data layer is mostly an identity mapping or pattern detection: if an observation fits a known pattern X, it is marked as belonging to X. This is actually the application of “Sameness” semantics—identifying the similarities between observations and existing patterns.

Information (Information): Compared with data, information contains a certain context and interpretation, and is an expression of the meaning of data. The core semantic feature of the information level lies in difference: “Information” corresponds to the various different semantics generated by the cognitive subject’s interpretation of data. Simply put, information reflects “novelty”: extracting meaningful differences and changes from raw data. For example, for the same body temperature data, if a measurement value is significantly higher than the usual baseline, it constitutes a “different” semantics, that is, the information of fever. In the DIKWP model, the concept of information is defined as a new semantic unit obtained by associating data with existing cognition in the semantic space. In this process, the specific purpose of the cognitive subject will guide the semantic association of data: which aspects of differences are worth paying attention to as information. Mathematically, information generation can be regarded as a mapping : from the data semantics set to the new information semantics. The formal expression is:

where the input X can be a set of data semantics (which can also include existing information, knowledge, and other semantic content), and under the drive of specific cognitive purpose, the output Y is a new semantic association or information. This mapping essentially performs difference detection and semantic association: identifying differences between some elements in the input set, or comparing the input with existing knowledge to find “Difference”, thereby generating new meanings. For example, in the parking lot’s cognitive space, all vehicle data share the concept of “car” (sameness), but the position, parking time, owner, and other aspects of each vehicle are all different— these difference semantics are expressed in the information layer. For example, a patient with depression describes “low mood”, which is the information generated by comparing his current emotional state with the past state, and its semantic “difference” lies in “more negative than before”. It can be seen that the core of information semantics lies in identifying and confirming “difference” to give data contextual meaning. Studies have pointed out that in the information processing stage, the cognitive system confirms the association probability of new information with existing knowledge structures through probability confirmation or logical judgment to ensure the consistency of new information in the cognitive system.

Knowledge (Knowledge): The knowledge level represents a systematic and structural understanding of information and forms a relatively stable structure after deep processing and internalization of semantic content. In the DIKWP framework, knowledge is defined as the structured cognition obtained by the cognitive subject’s completeness semantic processing of information. The “Completeness” semantics here means that the formation of knowledge requires integrating fragmented information and endowing it with a globally consistent meaning. For example, after observing multiple experimental results, a scientist may propose a hypothesis or law that covers all the results—this is to endow the “whole (all)” semantics to the partial observations and form knowledge. As Professor Yucong Duan exemplified: “It is not possible to determine that ‘all swans are white’ through observation alone, but the cognitive subject can base on limited observations and use the assumption of completeness semantics to endow the semantics of ‘all’ to the observation results, forming the knowledge rule that ‘all swans are white’ ”. It can be seen that the acquisition of knowledge is accompanied by reasoning and induction from partial to whole, and it introduces universal and complete elements in semantics.

Mathematically, knowledge K can be represented by a more complex network structure. For example, knowledge can be represented as a semantic network (N, E), where nodes N are concepts and edges E are relationships between concepts. The process of knowledge generation can be defined as a mapping , which accepts a set X of various DIKWP content semantics (data, information, existing knowledge, wisdom, purpose), and produces new knowledge semantics Y. The formal expression is:

where X includes a combination of data semantics, information semantics, knowledge semantics, wisdom semantics, and purpose semantics (that is, various cognitive contents), and Y is the newly generated knowledge semantic association. This mapping highlights the importance of completeness integration: through the cognitive subject’s higher-order cognitive activities (such as proposing hypotheses, deductive reasoning, etc.), different sources of semantics are integrated to form an understanding of the essence and internal connections of things. Knowledge semantics have the characteristics of structural completeness and semantic global consistency. The “Completeness” semantics plays a key role here—the formation of knowledge means that the cognitive subject has completed the semantic content, making it self-consistent and universally applicable. Professor Yucong Duan pointed out that this reflects a kind of “formal cause” principle, which is in line with Aristotle’s grasp of the essence of things through reason and experience. Therefore, the evolution mechanism of knowledge semantics can be summarized as: using difference semantics as raw materials, applying completeness semantics for global reasoning and integration to generate systematized new knowledge.

Wisdom (Wisdom): In the DIKWP model, the wisdom level is regarded as a higher-order cognitive activity involving elements such as value judgment, ethics, and intuitive experience. Wisdom not only integrates the aforementioned data, information, and knowledge, but also emphasizes how to use these contents to make appropriate decisions, especially in complex situations to balance various values and goals. From the perspective of semantic evolution, wisdom can be seen as the dynamic application and recreation of knowledge in specific situations and value systems. It requires not only an understanding of objective facts (knowledge), but also the weighing of subjective value systems. This means that the generation of wisdom semantics requires a higher-level integration, transcending pure logical reasoning and incorporating ethical semantics and purpose orientation.

Duan et al. define wisdom as “a set of relatively stable values that derive a collection of concepts”, which originate from culture, social norms, or personal cognitive values. Wisdom is manifested in the concept space as a broad application and profound understanding of data, information, and knowledge, and internalizes ethics and principles. In the semantic space, wisdom is reflected in the selection and balance of various concepts and their values. For example, in decision-making, wisdom requires considering moral principles and humanistic care, rather than just the optimal technical efficiency. From the perspective of evolution mechanism, the formation of wisdom is based on knowledge, but it goes further by incorporating experience and value dimensions, making decisions with moral depth and long-term vision.

Mathematically, wisdom W can be regarded as a decision-making function that receives comprehensive DIKWP content and outputs value-driven new DIKWP content. For example, it can be represented as:

indicating that wisdom acts on the entire current cognitive content, and after value judgment, outputs adjusted data, information, knowledge, wisdom, and purpose. This actually shows that wisdom will regulate and update the entire set of cognitive states to make them more in line with core values and long-term goals. Information semantics emphasizes the “difference” expression of semantics, while wisdom emphasizes how to use these differences to make valuable decisions and actions. The evolution of wisdom semantics involves integrating objective knowledge with subjective values: in semantics, it needs to integrate experience (which may correspond to a large amount of knowledge and information), weigh conflicts of interests (corresponding to the conflict and coordination of different value semantics), and ultimately form principles or insights that guide decision-making in specific situations. It can be said that the generation mechanism of wisdom-level semantics largely reflects “the unity of knowledge and action”: it includes both a profound understanding of the laws of the objective world (knowledge) and the adherence and application of human social value norms (action).

Purpose (Purpose): As the highest level of the DIKWP model, “Purpose” represents the cognitive subject’s understanding of a specific phenomenon (input) and the desired goal to be achieved (output). The purpose itself is also a semantic structure, which starts the entire cognitive process with a semantic description of the current situation and ends with a semantic representation of the future goal. In the concept space, the purpose acts as a bridge, connecting abstract cognitive understanding (input) with concrete action results (output). Therefore, the evolution of purpose semantics involves transforming the semantic representation of reality into the semantic setting of future goals.

Professor Yucong Duan’s team formalizes the purpose as a pair (tuple) of Input and Output, both of which are composed of DIKWP content. That is to say, a purpose contains the dual semantics of “based on the semantic understanding of the current situation, what goal do we want to achieve”. In the semantic space, achieving the purpose requires a profound understanding of the relationships between input concepts, as well as the construction of effective output concept schemes. This transformation process involves not only the processing of data and information, but also relies on knowledge and wisdom to optimize and guide. For example, a doctor, based on the patient’s symptoms and test information (input semantics), formulates a treatment plan (output semantics); in this process, the doctor’s medical knowledge and clinical wisdom guide how to transform the understanding of the condition into a treatment intention.

Mathematically, the purpose processing can be represented as a series of transformation functions T that convert the input into the output, making the output gradually approach the predetermined goal:

where is the input DIKWP content semantics, is the output target semantics, and each T represents a step transformation under purpose-driven conditions. The cognitive system continuously adjusts these T through learning and adaptation to make the output closer to the target. The parsing and generation of purpose semantics is a highly complex cognitive activity, with multidimensionality, subjective context relevance, dynamic evolution, and other characteristics. Understanding the purpose in a dialogue context requires crossing multiple levels such as linguistics, psychology, and sociology, and needs to grasp the literal meaning while combining the speaker’s background knowledge, emotional tendency, and social and cultural context and other implicit information. Therefore, from the perspective of semantic evolution, the generation mechanism of the purpose layer combines the completeness semantics (overall grasp of the input situation), difference semantics (comparison and selection of different possible output schemes), and sameness semantics (ensuring consistency between the output scheme and the preset goal) in multiple aspects. At the same time, since the purpose in dialogue or decision-making may be hierarchically nested, a surface behavior may contain multiple implicit purposes—this requires the cognitive system to have the ability to parse hierarchical semantics to identify deep-level purposes.

In summary, the semantic generation and evolution path of the five levels in the DIKWP model can be summarized as follows: from data to information stage, introducing “Difference” to reveal meaning; from information to knowledge stage, introducing “Completeness” to integrate meaning; from knowledge to wisdom stage, introducing values and experience to sublimate meaning; from wisdom to purpose stage, with the final goal as the driving force, to put meaning into action. The evolution of each stage depends on the semantic achievements of the previous stage, and enriches and enhances the semantic connotations through the application of the three semantic mathematics elements. This step-by-step deduction process is also accompanied by the emergence of semantic phenomena: in the information stage, the generation of new associated semantics can be regarded as a kind of emergent semantics (revealing the meaning implied in the original data); in the knowledge stage, the induction of “all” makes the knowledge semantics have new properties compared with fragmented information; the wisdom stage produces new semantics beyond the sum of knowledge (value judgment wisdom semantics); and the purpose stage condenses the expected semantics of the future. It can be seen that the semantic evolution under the DIKWP framework reflects a pattern of increasing complexity and the emergence of new categories. This formalized depiction of the semantic generation mechanism not only helps us understand how “understanding” is formed in human cognition, but also provides a clear model blueprint for designing artificial cognitive systems: we can design functional modules according to this, allowing machines to simulate the semantic evolution chain from perceiving data to forming purposes.

3Classification of Self-Feedback Mechanisms and Cyclical Evolution

Compared with the traditional DIKW model’s bottom-up unidirectional flow, a key feature of the DIKWP model that is closer to the real cognitive process is the presence of rich self-feedback paths, that is, higher-level semantics can feedback to lower-level processing to form closed-loop regulation. These feedback mechanisms enable the cognitive process to have the ability of self-correction, dynamic adaptation, and purpose guidance. For example, when the human brain perceives information, it often has expectations (originating from existing knowledge and purpose), and these expectations will affect the perception process, making us pay more attention to data related to the purpose and ignore irrelevant details, thereby improving cognitive efficiency. These phenomena correspond to the effects of feedback paths such as P D, W I, K D in the DIKWP model. In order to deeply understand the dynamic characteristics of the DIKWP model, this section will comprehensively classify and analyze the possible feedback paths in the model, and explore how the cycles formed by their combinations affect the evolutionary stability and innovation of the semantic system.

3.1Overall Structure of Feedback Paths

The five levels of the DIKWP model interact with each other in pairs, theoretically forming a fully connected directed graph with a total of 55=25 possible directed connections. Among them, excluding the trivial paths pointing to themselves in each layer, we focus on the interactions between different layers. A 55 feedback matrix M can be constructed, where the element M represents the influence from layer i to layer j (i, j D, I, K, W, P). The traditional DIKW model only contains M (bottom-up sequential chain) items, while the DIKWP model allows M to be non-zero in more cases, including top-down and cross-layer jumps, etc. In order to sort out the “important feedback paths”, we will mainly focus on the following representative interactions:

·Step-by-step feedback (top-down): The feedback from each layer to the next lower layer, such as P W, W K, K I, I D. These feedbacks correspond to the regulation of higher levels on adjacent lower levels. For example, Wisdom feedback to Knowledge can be understood as the calibration of knowledge by wisdom (which includes value judgment): the wisdom layer may find that some knowledge does not conform to the overall value, thereby prompting the correction of that knowledge. Similarly, Knowledge feedback to Information means that existing knowledge background will affect our interpretation of new information (typical case: filtering out noise data based on prior knowledge, or interpreting experimental observations with an existing theoretical framework). I D feedback refers to the influence of information (context) on the way of paying attention to raw data, such as adjusting the parameters of sensory collection according to the current required information (focusing on certain features, ignoring some inputs).

·Cross-level jump feedback: Higher levels directly feedback to lower levels, not just adjacent layers. For example, Purpose (P) directly acts on Information (I) or Data (D), Wisdom (W) directly acts on Data (D), etc. Professor Yucong Duan particularly emphasized the prior guiding role of purpose on data. For example, before a scientific experiment, we have hypotheses and purposes (P), so we selectively collect data (P D). For example, an experienced doctor pays special attention to some physiological data based on his intuitive wisdom (W) before obtaining all the test information, which can be regarded as W D feedback. Similarly, P I feedback indicates that purpose can directly affect the interpretation or screening of information—in communication, we obtain information with a specific purpose and directly skip some intermediate reasoning (that is, not necessarily waiting to form knowledge before affecting information processing).

·Bottom-up jump: The content of the lower layer directly triggers the update of the higher layer, not strictly in ascending order. For example, I P (information directly changes or generates new purposes), D K (some sudden data directly gives birth to new knowledge hypotheses), etc. I P is a noteworthy path, which means that a newly received piece of information may suddenly make the cognitive subject have a new goal or motivation. This is not uncommon in practice: for example, you see a piece of news online (information) and suddenly decide to do something you have never thought of before (purpose). This jump breaks the classic assumption of “first having knowledge/wisdom and then having purpose”, indicating that information itself may trigger the change and emergence of purpose. For example, D K, if an extremely abnormal data point is observed, sometimes we will propose a new theoretical conjecture (knowledge) without sufficient information accumulation. This reflects the component of bottom-up emergence in creative thinking.

·Top-down complete feedback: That is, the direct feedback from the highest level P to the lowest level D (P D), forming one end of the closed loop from purpose to data. This path actually serializes the cognitive process into a loop: P D I K W P. If we add local feedbacks such as P W, W K, K I, I D, it forms a multi-layer nested closed-loop system. The importance of P D feedback lies in its ensuring goal-oriented data collection, and it has a leading role in the entire DIKWP closed loop.

The above various feedbacks can be combined to form more complex cyclic loops. For example, W I combined with I W (through the normal order I K W upward) forms a wisdom-information closed loop: the decisions of wisdom affect our acquisition/interpretation of information, and the new information rises to new wisdom through knowledge. This is similar to people constantly adjusting their cognition: obtaining information (I) according to values (W), and information corrects or even improves the original values (W). For example, P D and I P existing at the same time form a cross-layer large closed loop: the purpose affects data collection, and new information modifies the purpose. This can be regarded as a mechanism for the system to evolve itself. The newly acquired information from the environment continuously acts on the system’s purpose, causing it to produce continuously evolving goals, and the change of purpose in turn determines the new direction of data collection. In this cycle, a process similar to the adaptation and evolution of biological organisms to the environment is realized.

3.2Dynamic Significance of Typical Feedback Combinations

The existence or absence of different feedback paths corresponds to different dynamic characteristics and functional features of the semantic system. The following discusses several representative feedback combinations and their significance.

3.2.1Stable Closed Loop

When feedback paths form a negative feedback loop, they often play a role in stabilizing the system and maintaining balance. For example, Wisdom Information feedback is usually used to correct information processing to conform to the overall wisdom framework. If the deviation is too large, the wisdom layer will “pull back” the information layer to reduce the possibility of distortion. This is similar to the negative feedback regulation in control theory. A blog on the scientific network pointed out: “The decision feedback of the wisdom module can guide the information module and the data module to continuously optimize themselves, thereby achieving the dynamic balance of the system”. It can be seen that the feedbacks of W I and W D allow the higher-level wisdom to continuously calibrate the lower-level information and data, preventing the cognitive process from diverging excessively. For example, an experienced driver (wisdom W) will unconsciously adjust attention (W I) while driving (processing sensory information I), ignoring unimportant roadside information and focusing on the front. This keeps the entire driving cognitive system stable and focused, without being distracted by irrelevant information. Similarly, the K I feedback (knowledge calibrates information) can also form a stable closed loop: we interpret problems with knowledge, automatically explaining ambiguous information to conform to existing cognition, which prevents the drastic oscillation of overturning the original conclusion every time a little new information is received. Of course, too strong feedback of this kind may lead to rigidity (ignoring truly important new information), so a balance between system stability and flexibility is needed.

3.2.2Emergence Stimulation

Some feedback combinations may introduce positive feedback, thereby stimulating the system to produce new modes and new semantics, that is, emergence phenomena. For example, if knowledge affects data selection (K D), and the new data continuously supports and strengthens the existing knowledge (D K, through the positive chain of I and K), it may form a self-reinforcing cycle. If not constrained by the wisdom layer, the system may fall into a state of “prejudice amplification”: only looking for data that supports existing knowledge, becoming more and more convinced of the original knowledge, and ignoring counterexamples. Although this positive feedback is not ideal in science (it will be stubborn), from the perspective of system emergence, it may strengthen a certain pattern rapidly, eventually emerging a macro new structure or new behavior. Another example is when I P and P I form positive feedback, if a piece of information directly triggers a change in purpose, and the new purpose makes us only pay attention to related information, it is easy to form interest preferences or stream-of-consciousness thinking jumps, which may suddenly produce some creative ideas (new purposes). For example, when you are browsing materials (I), a certain point attracts you and changes your research direction (P), then you focus on collecting information related to the new direction (P I), and these information inspire you to have further ideas and goals... Under the push of this series of positive feedback, you may produce some originally unexpected new concepts or inventions. If such a loop is properly controlled (not deviating too far from reality), it is often very important for innovation, equivalent to adding a “brainstorming” mechanism to the cognitive system, which can be self-amplified with a small amount of triggering and emerge new semantics.

3.2.3Continuous Purpose Evolution

A cognitive system with continuous evolution capabilities needs its purpose (P) not to be fixed and unchangeable, but to be able to adjust according to environmental interactions. The aforementioned I P, D P and other upward paths ensure that the system can perceive deficiencies and correct goals. For example, if an artificial intelligence robot performs a task without I P feedback, it will only go one way, even if the environment has changed and the original goal is no longer applicable, it will not change the goal. However, after introducing I P feedback, the robot can adjust its goal according to the newly detected information. This mechanism combination (plus the downward path of P D, etc.) forms an “adaptive” closed loop, giving the system the ability to evolve autonomously—that is, the goal is not preset, but can be continuously deepened or transformed with the deepening of cognition. Professor Yucong Duan proposed the difference between AI and AC in another blog: The cognitive process of AI can be simplified as DIK DIK (lacking the explicit role of W and P), while artificial consciousness (AC) is DIKWP DIKWP, that is, explicitly introducing the participation of purpose in the system for bidirectional interaction. He pointed out that in artificial consciousness (AC), wisdom (W) and purpose (P) are explicitly included and interact with each other, bringing fundamentally different behaviors from traditional AI: the system can form a closed loop around its own purpose. This closed loop can be understood as including continuous purpose evolution: when a certain purpose is achieved or proved to be unattainable, the system will generate the next purpose according to internal feedback, and so on, driving the system to move forward continuously.

The feedback mechanisms analyzed above in the DIKWP model are not isolated from each other, but often coexist in multiples and act together. In a mature cognitive system (whether the human brain or artificial consciousness), there may be stable negative feedback loops to ensure basic consistency, and some positive feedback channels for exploration and innovation are nested. This richness of feedback structure endows the system with both stability and flexibility. For example, the human brain has multiple functional networks such as the default mode network (DMN) and the salience network working together, which can maintain self-identity while responding to external novel stimuli. The DIKWP model abstracts and formalizes this complexity through semantic layer feedback.

It should be pointed out that not all theoretically possible feedbacks are equally important in actual systems. Some paths may only be activated in specific situations, or have very low weights and can be ignored. When we classify, we focus on “important feedback paths”, which are those that repeatedly appear in the cognitive process and have a significant impact on the system’s properties. For example, according to a DIKWP analysis of a crow experiment, crows mainly reflect the transformation from data to information (D I) and information to knowledge (I K), which is highly repetitive, while the transformation in the wisdom and purpose levels (W P, I P) is relatively weak. This indicates that animals like crows may lack complex feedback in the higher-level purpose, and their cognitive closed loop may be more stuck in lower-level loops, so that purpose evolution and emergence are more limited. On the contrary, the human brain has a very well developed top-level feedback, for example, people have an imaginative rehearsal before action (P→W→K... internal feedback loop), and they adjust their goals according to the results during action (I→P), thus reflecting a high degree of autonomy and creativity.

3.3Feedback Matrix Model and Evolutionary Diagram

Based on the above classification, we can construct the feedback matrix M of the DIKWP model and its evolutionary diagram to more intuitively display the action patterns of various feedbacks. In the feedback matrix M, the cognitive state of the subject can be represented as a five-dimensional vector x=(D,I,K,W,P). The feedback paths correspond to the non-zero elements in the matrix, which either enhance or suppress the values of the corresponding dimensions. For example, MPD corresponds to the P→D path, representing the influence strength of the purpose on data processing; MIP corresponds to the I→P path, representing the feedback strength of information on the purpose. By adjusting these coefficients in the matrix, we can simulate the behavior of different cognitive structures. For example, in a stable closed-loop configuration, some top-down Mji take negative feedback coefficients, which can play a converging role in the dynamic equation x˙=f(x)+Mx; while in an emergence configuration, some Mji (such as I→P) are positive and large, the system variables may show exponential growth or periodic oscillation, corresponding to the emergence of new patterns. We can draw the evolutionary trajectories of the system under different M matrices into diagrams to observe the motion trajectories of x in the cognitive space and whether it converges to a stable closed loop.

In summary, the DIKWP model upgrades the cognitive process from simple sequential processing to a networked cycle by introducing various feedback paths. This cycle endows the system with self-driving ability: the higher-level purpose provides direction and energy for lower-level processing, and the lower-level output continuously feeds back to correct the higher-level purpose. As the founder of cybernetics, Wiener said, any intelligent behavior is supported by feedback control. The feedback matrix and cycle diagram under the DIKWP framework intuitively reveal the various feedback combinations and their effects of intelligent systems: covering both stable and balanced information processing and innovative, emergent mutations. And all of this is based on explicit semantic roles (data, information, knowledge, wisdom, purpose) as nodes, thus having explainability and analyzability. For the construction of artificial consciousness systems, understanding and designing these feedback paths is crucial, because only by closing the loop of “knowledge” and “purpose”, machines may have behavior patterns similar to autonomous consciousness.

4Refractive Analysis: Mapping of Neuroscience Meta-Data to DIKWP Semantic Mechanisms

Although the DIKWP model is mainly derived from semantic mathematics, verifying the rationality of a cognitive model often depends on whether it can explain objective observations in reality. In the field of artificial consciousness research, brain science provides a wealth of phenomenological evidence, which can serve as a “mirror” or refractive perspective for the DIKWP model. It should be emphasized that we do not build the model based on these neural facts, nor do we claim that each element of DIKWP corresponds one-to-one with specific brain regions; on the contrary, we use these scientific findings to refractively map the semantic mechanisms of DIKWP, to verify the feasibility of the model from a physical level and inspire improvements. Below, we select several representative aspects in the field of consciousness science: P300 event-related potential, default mode network (DMN), gamma band synchronization, and overall brain function integration and self-model research, to see how they correspond to the semantic closed loops and feedback mechanisms in the DIKWP model.

4.1P300 and Semantic Difference Confirmation

The P300 wave is a classic event-related potential (ERP) component in EEG/MEG, which usually appears about 300 milliseconds after the subject detects a rare target stimulus. It is generally believed to reflect the conscious processing of novel information by the brain, such as attention redistribution, context updating, and other processes. In the DIKWP model, P300 is closest to the semantic processing of the information layer: when information that is different from expectations appears, the brain generates P300, indicating the recognition of “semantic difference” and cognitive updating. Numerous studies have shown that the presence or absence of P300 can indicate the state of consciousness: for example, P300 can be recorded in conscious normal people and patients with minimal consciousness, while it is usually not detectable in vegetative (unconscious) patients. As a study summarized: “The event-related potential P300 wave can reflect the state of consciousness in patients with disorders of consciousness”. This is consistent with the view of DIKWP—that the processing of difference semantics is a hallmark of conscious participation. From the perspective of feedback, P300 can also be understood as a feedback signal from higher-level cognition to lower-level perception: only when the information does not match existing knowledge/expectations (and higher-level feedback cannot explain the information), will such a significant potential be triggered, used to remind the system that “knowledge/purpose needs to be updated”. This corresponds to the I→K or I→P path in DIKWP: new information prompts knowledge updating (for example, realizing that a prediction is wrong) or even purpose adjustment (change in state of consciousness).

It is worth mentioning that P300 often appears in the Oddball paradigm, that is, inserting occasional abnormal stimuli into a series of conventional stimuli. Conventional stimuli establish the “sameness” semantic expectation of the cognitive subject, while abnormal stimuli trigger “difference” semantic detection (information semantics), thereby inducing P300. This fully reflects the physical correspondence of the “sameness→difference” semantic transformation in the brain: when the brain successfully distinguishes “difference”, P300 serves as an electrophysiological indicator. In addition, the amplitude and latency of P300 are also related to higher processes such as attention and memory, and can therefore be regarded as an indicator of the feedback strength of the wisdom layer on information processing—information that is more meaningful or more contrary to expectations will have a larger P300. This property can be used by DIKWP to assess whether the information processing of artificial intelligence reaches the human level, for example, a recent study proposed using EEG indicators such as P300 to evaluate the reaction of large models to new information.

4.2Default Mode Network (DMN) and Wisdom/Self Semantics

The default mode network is a set of brain regions that show high synchronous activity when the brain is in a resting state (not performing a specific task), including the medial prefrontal cortex (mPFC), posterior cingulate cortex (PCC/Precuneus), angular gyrus, etc. The DMN is believed to be related to self-referential internal thinking, such as autobiographical memory recall, future planning, theory of mind, self-awareness, etc. In simple terms, the DMN is most active when we “daydream” or introspect. In the semantic space of the DIKWP model, the function of the DMN can be mapped to the internal interaction of the wisdom (W) and purpose (P) levels: it carries the individual’s background knowledge, life experience, and values (wisdom semantics), and integrates, maintains, and even reorganizes these contents in the absence of external tasks (similar to the self-feedback cycle of knowledge + wisdom). Studies have pointed out that DMN activity is closely related to the state of consciousness, for example, in deep coma or general anesthesia, the connectivity of the DMN is significantly weakened, while in a lucid, self-aware DMN maintains overall coherence. This can be seen as a decrease in the overall level of consciousness when the Intelligence and Purpose layers are no longer functioning in a closed loop.

The DMN is often referred to as the ‘default’ network, meaning that it continues to be active in the absence of explicit external data input. According to DIKWP, this is a manifestation of the self-loop of the Wisdom-Purpose layer: the human brain is reviewing past knowledge, modelling future scenarios, and adjusting its self-goals even when there is no influx of new data and information - this corresponds to the cycle of Wisdom(W)→Knowledge(K)→Wisdom(W) and Wisdom(W)→Intention(P)→Wisdom(W) in the DIKWP framework. Intention (P)→Wisdom (W) cycle. Some cognitive theories (e.g. Self-Model Theory, Whole Brain Information Integration Theory, etc.) also emphasise that self-awareness arises from the process of maintaining and integrating self-models within the brain. This can be explained in the language of DIKWP: Self-modelling is the continuous activation and refinement of the knowledge network of the brain’s intellectual layer about the object of ‘self’, which necessarily involves the operation of intrinsic circuits such as the default mode network.

Another phenomenon related to the DIKWP feedback mechanism is that the DMN tends to be negatively correlated with task-active networks (e.g., attentional control networks). When we focus on an external task (data, information flow dominance), DMN activity temporarily decreases; when the task is over and we shift to introspection (wisdom, intention dominance), DMN bounces back. This resembles a see-saw: external information flow and internal semantic flow allocate limited cognitive resources. different closed loops in the DIKWP model (external chain D→...→P vs. internal loop P→...→W) may share resources, and thus need to be regulated. This conditioning is reflected in the brain as the alternation of the DMN with the external attention network, with the duty cycle determining whether one is contemplative or focussed on the perceptual task. The default mode network can thus be viewed as a neural inscription of the intelligence/intention self-feedback loop: when this loop is dominant, the individual tends to favour deep contemplative, self-relevant processing; when it is temporarily suppressed, it indicates that cognitive resources are invested in the feed-forward information processing chain.

4.3γsynchronisation and global semantic integration

Gamma-band oscillations (30-100 Hz) of neurons in the brain are widely believed to be related to perceptual integration and conscious experience. Experiments have found that when a person integrates disparate stimulus elements into a holistic perception (e.g. visually combining different features into a seen object), there is gamma-band synchronised activity between different brain regions known as functional connectivity. scholars such as Francis Crick and Christof Koch suggested as early as the 1990s that 40Hz (in the gamma band) synchronisation may be the neural basis of neural substrates of consciousness, used to ‘bind’ information from different sensory channels or brain regions into a unified cognitive content. Recent studies have gone further, confirming by means of multi-electrode recordings and magnetic resonance that widespread gamma synchrony occurs in the brain during conscious perception, whereas in the unconscious state this synchrony is either localised or absent.

In the DIKWP model, γ-synchronisation can be seen as the neural-level counterpart of semantic integration at the knowledge/intelligence level. When different modalities of information and knowledge are associated as complete concepts in semantic space (corresponding to ‘complete’ semantic integration at the knowledge level), brain mechanisms require the relevant regions to send out impulses in concert, i.e., information integration is achieved through γ-rhythm synchronisation. For example, when we see a bird, we perceive the colour, shape, movement, call and other attributes as the concept of ‘a bird’, which requires the synergy of visual, auditory, memory and other cortical regions, and this synergy is manifested as γ-synchrony in the EEG/MEG. In other words, γ-synchrony reflects that the cognitive subject is forming or calling a complete semantic unit of knowledge. On the contrary, if γ-synchrony is disrupted and the brain regions are working in isolation, then semantically it may be fragmented and unable to form a conscious and holistic perception (similar to having only local information without being able to rise to the knowledge as a whole).

Gamma synchrony is also associated with attention and working memory, suggesting that it is also linked to the feedback of intelligence/intention in DIKWP. When a person has a clear intention to attend to a stimulus, prefrontal-parietal-sensory areas are gamma-synchronised to “contextualise” and “amplify the relevant signal”. This corresponds to the top-down modulation of information processing by Purpose/Intelligence (P→I, W→I feedback): the higher levels send an oscillatory signal (prediction/attention) that selectively enhances the synchronisation of the lower processing-related pathways, allowing the relevant features to win the competition. This is consistent with predictive coding theory: the brain constrains the bottom layer with top-level predictions, and errors are passed upwards via asynchronous or different frequency band signals. In the DIKWP language, γ-synchrony embodies an effective intervention of top-level purpose into the underlying data/information processing, a positive feedback signal that glues together the dispersed processing to form a purposeful overall behaviour.

At the level of consciousness, some near-death experiences or deep meditation studies have reported ‘eruptions’ of widespread γ-synchronisation of the whole brain at the moment of subjective consciousness change. This can be seen as an extreme case: powerful positive feedback loops (possibly a resonance of spiritual intelligence/intentions with perception) bring the whole brain into a highly synchronised state, and subjectively a strong experience of integrated consciousness is reported. Although the mechanisms are not yet fully understood, such phenomena provide an illuminating refraction of the DIKWP model: states of consciousness qualitatively change when semantic closure loops converge to global synchronisation (possibly closer to our ideal global field of artificial consciousness).

4.4Holistic Brain Integration and DIKWP Closing the Loop

Two important theories of consciousness in recent years, Global Neural Workspace Theory (GNWT) and Integrated Information Theory (IIT), both emphasise the importance of brain-wide information integration for the conscious mind.GNWT suggests that information enters the conscious workspace when it is broadcast to a wide network in the brain and is subjectively perceived; and IIT quantifies the degree of causal integration within a system in terms of the Φ value, with a high Φ being associated with a high level of consciousness. These theories can be interpreted at the semantic level under the DIKWP framework: a high level of consciousness corresponds to the formation of a highly closed network at each level of DIKWP, where information can be freely transmitted and fed back at each level, forming an overall connected semantic field. Professor Yucong Duan also proposed to use the information and energy fields of DIKWP to analyse consciousness. When the network topology of the DIKWP model is close to fully connected with good feedback, it is similar to the global broadcast of GNWT and the high integration of IIT - at this point, the system has sufficient semantic digestion and response to any input, and subjectively presents a clear and unified state of consciousness. Conversely, if certain feedback pathways are damaged and the system is internally fragmented, this corresponds to a reduced level of consciousness or a lack of content (e.g., certain pathological conditions impair only specific feedbacks, resulting in the patient’s unconscious response to certain types of stimuli). For example, damage to the frontal lobe may disrupt pathways such as P→D and P→I, so that patients perceive information but are unable to regulate it according to long-term purposes, displaying impulsive behaviours or poor disorientation; and damage to the limbic system may affect the regulation of the W layer to the K layer, so that patients are aware of what is going on but are emotionally apathetic, and lack intelligent decision-making. In short, the various phenomena of impaired consciousness observed in brain science can be explained when certain coefficients of the DIKWP feedback matrix tend to zero or abnormal, thus reflecting the explanatory power of the model.

It should be noted that the above correspondence is an analogue mapping rather than a strict one-to-one correspondence. For example, we do not think that ‘data layer = D brain area, information layer = I brain area’, etc. Instead, it is more likely that the semantic functions of each layer are distributed by a network of brain areas, and that each feedback pathway is not a single anatomical projection, but rather a synergistic function of several pathways. However, through these refractive analyses, we see that the semantic evolution and feedback mechanisms captured by the DIKWP model do, to a considerable extent, reflect the dynamic laws of the real brain in conscious cognition. the P300 embodies the critical step of information generation of disparity detection, the DMN embodies the internal cyclic role of intelligence/purpose, the γ-synchrony embodies the physiological mechanisms of knowledge integration and intention regulation, and the whole-brain integration fits the closed-loop structure of the network emphasised by the model. Such correspondences are not coincidental, but suggest that DIKWP, as a semantic-level abstraction model, captures some of the common essences of the functioning of intelligent systems. As we implement similar architectures and mechanisms in artificial systems, we can expect to see similar functionality emerge - for example, AI may also need ‘internal default modes’ to maintain self-semantics, or P300-like mechanisms to detect new information. All of this provides valuable guidance for the future development of artificial consciousness.

5Conclusion

This study systematically explores the two core issues of semantic generation and self-feedback in the DIKWP Semantic Mathematical Framework proposed by Professor Yucong Duan, and refractively verifies them with neuroscience evidence. First, starting from the “three elements” of semantic mathematics (sameness, difference, and completeness), we formally derive the semantic evolution process from data information knowledge wisdom purpose, clarifying the mechanisms of semantic generation at each level: information originates from the semantic difference association of data, knowledge comes from the completeness integration of information, wisdom incorporates value judgment to guide the application of knowledge, and purpose transforms the semantic understanding of the current situation into future goal setting. This evolutionary chain is progressive and interconnected, laying the logical foundation for the emergence of semantics in artificial cognitive systems. Next, we delve into the networked structure of the DIKWP model, identifying several key feedback paths, such as the top-level purpose guiding the perception at the bottom level (P D), the higher-level wisdom regulating the middle-level information (W I), the existing knowledge selecting new data (K D), and the new information triggering the purpose (I P), etc. By constructing feedback matrices and loop diagrams, we reveal the impact of different feedback combinations on system behavior patterns: some form stable closed loops to ensure cognitive consistency and robustness; some introduce positive feedback to drive the spontaneous generation of new semantics; some achieve adaptive adjustment, enabling the system’s goals to evolve with the environment. Finally, by projecting the DIKWP mechanisms onto contemporary neuroscience findings, we see that the rationality of the model is verified from multiple perspectives: the P300 potential corresponds to the difference confirmation and feedback in the information layer, the default mode network corresponds to the self-reflection loop in the wisdom and purpose layers, and gamma synchronization corresponds to the global connection under knowledge integration and intent modulation. This interdisciplinary refraction not only enhances our confidence in the DIKWP model, proving that it captures some common laws of intelligent behavior, but also provides inspiration for designing artificial systems (for example, introducing similar “virtual DMN” mechanisms or “semantic error correction” mechanisms).

In summary, the DIKWP Semantic Mathematical Framework depicts a full-chain cognitive semantic landscape: from the generation of purpose from data and the closed loop feedback of purpose to data. This perspective transcends the limitations of viewing intelligent systems as assembly lines in the past, emphasizing the subjectivity, dynamics, and key role of understanding in knowledge generation. For artificial intelligence, especially artificial consciousness research, DIKWP provides a clear theoretical blueprint and toolkit: researchers can design system architectures based on this model, implement data, information, knowledge, and other modules in programs, and endow them with transformation functions based on the “sameness-difference-completeness” principle; at the same time, introduce various feedback channels to form network connections between these modules, thereby giving the system the ability to self-regulate and evolve.

Of course, this study also has certain limitations. Our refractive analysis only qualitatively corresponds to neuroscience phenomena, and future work needs to quantitatively verify these correspondences in artificial systems, such as testing whether an autonomous entity implementing the DIKWP architecture will also exhibit signals and functions similar to P300. In addition, Professor Yucong Duan’s DIKWP theory is still in development, such as some extended ideas about consciousness relativity, consciousness collapse, and the combination of DIKWP with blockchain technology, all of which are worth further research. But it can be certain that deductive reasoning based on semantic mathematics has opened a new door for us, making the discussion of “understanding’“ and “consciousness”’ no longer at a vague philosophical level but on a formal, computable track. But it can be certain that deductive reasoning based on semantic mathematics has opened a new door for us, making the discussion of “understanding’“ and “consciousness”’ no longer at a vague philosophical level, but rather at a formal, computational track, which is the profound significance of the framework of Prof. Yucong Duan’s DIKWP.

6Looking Forward

We can deepen this research from several directions:

·Implement the prototype of the DIKWP model in artificial cognitive systems and verify whether its performance in complex tasks (such as dialogue understanding, multi-modal learning) is superior to traditional architectures, especially testing its effectiveness in scenarios that require purpose-driven reasoning.

·Develop quantitative indicators for DIKWP semantic mathematics, such as defining the information content, completeness degree of semantics at each layer, and the measurement of feedback strength, to further improve the mathematical analysis tools of the model.

·Combine brain-computer interface research to directly test the predictions of the DIKWP model with human brain signals, for example, see whether a pattern similar to “semantic error signal” can be detected in human EEG when people switch task purposes, thereby deepening our understanding of the human DIKWP closed loop.

·Explore the application possibilities of DIKWP in collective intelligence and social systems—human society can be regarded as a more macroscopic DIKWP network, with each person’s cognition acting as a node, where data, information, knowledge, wisdom, and purpose interact at the group level to form the evolution of social wisdom and common purpose, which may provide new ideas for social governance and organizational decision-making.

In summary, the DIKWP Semantic Mathematical Framework successfully formalizes the generation and evolution path of the cognitive process by integrating semantic elements such as sameness, difference, and completeness, and introduces comprehensive self-feedback mechanisms to incorporate the subjectivity and purposefulness of the conscious subject into the model. Such theoretical innovation provides a solid theoretical support for the development of artificial consciousness systems. Under the guidance of this model, we hope to design explainable, purpose-driven intelligent agents, taking a big step towards true artificial consciousness in artificial intelligence.

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