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)

The Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework provides a structured approach to model cognitive processes mathematically. By representing each stage of cognition—Data, Information, Knowledge, Wisdom, and Purpose—we can simulate how humans process information and make decisions.

In this analysis, I will:

• Apply DIKWP principles to a specific cognitive task.

• Use mathematical representations to model each stage.

• Demonstrate how this approach simulates human cognitive processes.

An AI system is designed to simulate a doctor's cognitive process in diagnosing a patient with symptoms of fever, cough, and shortness of breath.

Definition: Raw, unprocessed facts without interpretation.

In this context:

• Patient's symptoms and vital signs.

Mathematical Representation:

Let $D$ be the set of observed data:

D={s1,s2,s3,v1,v2,v3}D = \{ s_1, s_2, s_3, v_1, v_2, v_3 \}D={s1​,s2​,s3​,v1​,v2​,v3​}

Where:

• s1s_1s1​: Fever (38.5∘C38.5^\circ C38.5∘C)

• s2s_2s2​: Cough

• s3s_3s3​: Shortness of breath

• v1v_1v1​: Heart rate ($100$ bpm)

• v2v_2v2​: Blood pressure ($120/80$ mmHg)

• v3v_3v3​: Oxygen saturation ($92\%$)

Definition: Processed data with context and meaning.

Processing:

• Interpreting symptoms and vitals in a medical context.

• Recognizing patterns or abnormalities.

Mathematical Representation:

Transform $D$ into $I$ using a function fIf_IfI​:

I=fI(D)I = f_I(D)I=fI​(D)

For each data point, assign meaning:

• i1=Fever above normal rangei_1 = \text{Fever above normal range}i1​=Fever above normal range

• i2=Presence of coughi_2 = \text{Presence of cough}i2​=Presence of cough

• i3=Shortness of breath indicates possible respiratory issuei_3 = \text{Shortness of breath indicates possible respiratory issue}i3​=Shortness of breath indicates possible respiratory issue

• i4=Elevated heart ratei_4 = \text{Elevated heart rate}i4​=Elevated heart rate

• i5=Normal blood pressurei_5 = \text{Normal blood pressure}i5​=Normal blood pressure

• ( i_6 = \text{Low oxygen saturation} }

So:

I={i1,i2,i3,i4,i5,i6}I = \{ i_1, i_2, i_3, i_4, i_5, i_6 \}I={i1​,i2​,i3​,i4​,i5​,i6​}

Definition: Assimilated information that is understood and can be applied.

Knowledge Base:

• Medical knowledge about diseases presenting with these symptoms.

• Understanding of pathophysiology.

Mathematical Representation:

$K$ includes relevant medical conditions and their associated symptoms.

Define a set of possible diagnoses DpossibleD_{\text{possible}}Dpossible​:

Dpossible={d1,d2,d3}D_{\text{possible}} = \{ d_1, d_2, d_3 \}Dpossible​={d1​,d2​,d3​}

Where:

• d1d_1d1​: Influenza

• d2d_2d2​: Pneumonia

• d3d_3d3​: COVID-19

Also, knowledge of symptom-disease relationships $S$:

S={(si,dj)∣si is associated with dj}S = \{ (s_i, d_j) \mid s_i \text{ is associated with } d_j \}S={(si​,dj​)∣si​ is associated with dj​}

Definition: The judicious application of knowledge with insight.

Application:

• Prioritizing diagnoses based on prevalence, patient history, and symptom severity.

• Considering current epidemiological data.

Mathematical Representation:

Assign weights to each possible diagnosis based on probability:

w(dj)=fW(I,K)w(d_j) = f_W(I, K)w(dj​)=fW​(I,K)

Where fWf_WfW​ evaluates the likelihood of each diagnosis.

For example:

• w(d1)=0.2w(d_1) = 0.2w(d1​)=0.2

• w(d2)=0.3w(d_2) = 0.3w(d2​)=0.3

• w(d3)=0.5w(d_3) = 0.5w(d3​)=0.5

So, COVID-19 (d3d_3d3​) is the most probable diagnosis.

Definition: Intentional action guided by wisdom to achieve goals.

Goal:

• To accurately diagnose and treat the patient.

Action Plan:

• Order confirmatory tests (e.g., PCR test for COVID-19, chest X-ray).

• Initiate appropriate treatment protocols.

• Implement isolation procedures to prevent spread.

Mathematical Representation:

Define an action $A$ to maximize patient outcome $U$:

$P=\text{Select }A\text{ that maximizes }U\text{ given }W$

Collect patient data $D$:

D={Fever,Cough,Shortness of breath,Elevated heart rate,Normal BP,Low O2 saturation}D = \{ \text{Fever}, \text{Cough}, \text{Shortness of breath}, \text{Elevated heart rate}, \text{Normal BP}, \text{Low O}_2 \text{ saturation} \}D={Fever,Cough,Shortness of breath,Elevated heart rate,Normal BP,Low O2​ saturation}

Interpret data to form $I$:

• Recognize symptoms indicative of respiratory infection.

Use $K$ to generate possible diagnoses DpossibleD_{\text{possible}}Dpossible​ and associate symptoms using $S$.

Calculate weights w(dj)w(d_j)w(dj​) based on:

• Symptom matching.

• Current COVID-19 prevalence.

• Patient's exposure history.

Select actions $A$:

• Order COVID-19 test.

• Start supportive care.

• Advise patient on isolation.

Create a matrix $M$ where rows are symptoms sis_isi​ and columns are diseases djd_jdj​:

M=(s1s2s3s4s5s6)M = \begin{pmatrix} s_1 & s_2 & s_3 & s_4 & s_5 & s_6 \\ \end{pmatrix}M=(s1​​s2​​s3​​s4​​s5​​s6​​)

With values:

M=(111100111101111101)M = \begin{pmatrix} 1 & 1 & 1 & 1 & 0 & 0 \\ % Influenza 1 & 1 & 1 & 1 & 0 & 1 \\ % Pneumonia 1 & 1 & 1 & 1 & 0 & 1 \\ % COVID-19 \end{pmatrix}M=​111​111​111​111​000​011​​

Using Bayesian inference:

P(dj∣I)=P(I∣dj)P(dj)P(I)P(d_j | I) = \frac{P(I | d_j) P(d_j)}{P(I)}P(dj​∣I)=P(I)P(I∣dj​)P(dj​)​

Assuming equal prior probabilities and independence, we can calculate relative likelihoods.

Define a decision function $\delta$:

δ(I,K)=arg⁡max⁡djw(dj)\delta(I, K) = \arg\max_{d_j} w(d_j)δ(I,K)=argmaxdj​​w(dj​)

Select diagnosis with the highest weight.

The AI system encounters new data indicating a new symptom associated with COVID-19: loss of taste.

• Data (D′D'D′): New symptom s7=Loss of tastes_7 = \text{Loss of taste}s7​=Loss of taste.

• Information (I′I'I′): Recognize s7s_7s7​ as a symptom.

• Knowledge Update (K′K'K′):

Add s7s_7s7​ to symptom-disease associations:

S′=S∪{(s7,d3)}S' = S \cup \{ (s_7, d_3) \}S′=S∪{(s7​,d3​)}

• Wisdom (W′W'W′): Re-evaluate weights w′(dj)w'(d_j)w′(dj​) with updated knowledge.

• Purpose (P′P'P′): Adjust diagnostic and treatment protocols accordingly.

• Semantic Units:

• Symptoms (sis_isi​): Fever, cough, etc.

• Diseases (djd_jdj​): Influenza, pneumonia, COVID-19.

• Relationships: Associations between symptoms and diseases.

• Mathematical Representation:

• Each symptom and disease is a vector in high-dimensional space.

• Similar symptoms/diseases are closer in space.

• Concepts:

• Respiratory infections.

• Viral diseases.

• Diagnostic protocols.

• Formation:

• Concepts are clusters of semantic units.

• The AI system can navigate this space to reason about diagnoses.

• Pattern Recognition: Identifying symptom patterns matching certain diseases.

• Abstraction: Generalizing from specific symptoms to broader disease categories.

• Evaluating Options: Weighing potential diagnoses based on likelihood.

• Selecting Actions: Choosing the best course of action to achieve the desired outcome.

• Updating Knowledge Base: Incorporating new medical findings.

• Improving Decision Strategies: Refining diagnostic criteria based on outcomes.

By applying the DIKWP Semantic Mathematics framework, we have simulated the cognitive process of diagnosing a medical condition, mirroring how a human doctor might think, decide, and learn. This approach demonstrates how AI systems can use DIKWP principles to process data, apply knowledge wisely, and act with purpose.