Infant's Cognitive, Semantic, and Conceptual Spaces During Emotion Learning Using 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 continues the comprehensive simulation of an infant's cognitive development by focusing on the emotion learning stage, emphasizing the state changes in the cognitive space, semantic space, and conceptual space within the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework proposed by Prof. Yucong Duan. By detailing each incremental change as the infant interacts with emotional stimuli and social interactions, we illustrate how cognitive structures evolve during emotion learning. This step-by-step account provides a deep understanding of how exposure to emotions influences semantics and concepts, contributing significantly to the infant's overall cognitive and social development.

Table of Contents

1. Introduction

• 1.1 Overview

• 1.2 Objectives

2. Foundational Concepts

• 2.1.1 Cognitive Space

• 2.1.2 Semantic Space

• 2.1.3 Conceptual Space

• 2.1 Cognitive Spaces in DIKWP Semantic Mathematics

• 2.2 Mathematical Representation of Spaces

3. Simulated Scenario: Emotion Learning Stage

• 3.1 Setting and Characters

• 3.2 Overview of Developmental Timeline

4. Detailed State Changes in Emotion Learning

• 4.3.1 Cognitive State Expansion

• 4.3.2 State Changes per Interaction

• 4.2.1 Cognitive State Evolution

• 4.2.2 State Changes per Interaction

• 4.1.1 Initial Cognitive State

• 4.1.2 State Changes per Interaction

• 4.1 Stage 1: Initial Emotional Responses (0-6 Months)

• 4.2 Stage 2: Recognition of Others' Emotions (7-12 Months)

• 4.3 Stage 3: Expression and Regulation of Emotions (13-18 Months)

5. Mathematical Modeling of State Changes in Emotion Learning

• 5.1 Semantic Space Transformations

• 5.2 Conceptual Space Transformations

• 5.3 Cognitive Space Integration

6. Visualization of State Changes

• 6.1 Diagrams of Cognitive Spaces

• 6.2 Graphical Representation of Transformations

7. Discussion

• 7.1 Insights from Detailed State Changes

• 7.2 Implications for AI and Cognitive Science

• 7.3 Limitations and Future Directions

8. Conclusion

9. References

1. Introduction1.1 Overview

Emotional development is a critical aspect of an infant's overall growth, influencing social interactions, cognitive processes, and language acquisition. This document simulates the infant's cognitive development during the emotion learning stage, focusing on the state transitions within the cognitive, semantic, and conceptual spaces as modeled by the DIKWP Semantic Mathematics framework.

1.2 Objectives

• Detail every state change in the infant's cognitive, semantic, and conceptual spaces during emotion learning.

• Provide mathematical representations of these changes.

• Illustrate the evolution of cognitive structures influenced by emotional experiences.

• Enhance understanding of how emotion learning contributes to overall cognitive and social development.

2. Foundational Concepts2.1 Cognitive Spaces in DIKWP Semantic Mathematics2.1.1 Cognitive Space ($\mathcal{C}$)

• Definition: The overall mental space encompassing all cognitive processes, including those related to emotional perception and regulation.

• Components: Includes the semantic and conceptual spaces specific to emotional elements.

2.1.2 Semantic Space ($S$)

• Definition: A multidimensional space representing the meanings associated with emotional inputs and experiences.

• State Changes: Occur when new emotional semantic units are formed or existing ones are modified.

2.1.3 Conceptual Space ($C$)

• Definition: A structured space where emotional concepts are formed by organizing semantic units related to emotions.

• State Changes: Happen when new emotional concepts are created or existing concepts are updated.

2.2 Mathematical Representation of Spaces

• Emotional Semantic Units (sis_isi​): Represented as vectors in $S$ with attributes like facial expressions, tone of voice, physiological sensations.

• Emotional Concepts (ckc_kck​): Formed by functions mapping sets of emotional semantic units to vectors in $C$.

• State ($\sigma$): At any time $t$, the state of each space is σS(t)\sigma_S^{(t)}σS(t)​ and σC(t)\sigma_C^{(t)}σC(t)​.

3. Simulated Scenario: Emotion Learning Stage3.1 Setting and Characters

• Infant: Emma, from 0 to 18 months.

• Parents: Alice and Bob, who provide varied emotional interactions.

• Environment: Home setting with opportunities for emotional expression and social interaction.

3.2 Overview of Developmental Timeline

• Stage 1 (0-6 Months): Initial emotional responses; formation of basic emotional semantic units.

• Stage 2 (7-12 Months): Recognition of others' emotions; initial emotional concept formation.

• Stage 3 (13-18 Months): Expression and regulation of emotions; refinement of emotional concepts and integration with social understanding.

4. Detailed State Changes in Emotion Learning4.1 Stage 1: Initial Emotional Responses (0-6 Months)4.1.1 Initial Cognitive State

• Time t0t_0t0​:

• Cognitive Space (C(t0)\mathcal{C}^{(t_0)}C(t0​)): Minimal structure for emotional elements.

• Semantic Space (σS(t0)\sigma_S^{(t_0)}σS(t0​)​): Lacks emotional semantic units.

• Conceptual Space (σC(t0)\sigma_C^{(t_0)}σC(t0​)​): No emotional concepts formed.

4.1.2 State Changes per Interaction

Interaction 1: Comforting After Crying

• Emotional Input: Feeling of discomfort leading to crying (ddiscomfortd_{\text{discomfort}}ddiscomfort​), followed by parental soothing (dsoothingd_{\text{soothing}}dsoothing​).

• State Change in Semantic Space (ΔσS(t1)\Delta \sigma_S^{(t_1)}ΔσS(t1​)​):

• σS(t1)=σS(t0)∪{snegative_feeling(1),ssoothing_sensation(1)}\sigma_S^{(t_1)} = \sigma_S^{(t_0)} \cup \{ s_{\text{negative\_feeling}}^{(1)}, s_{\text{soothing\_sensation}}^{(1)} \}σS(t1​)​=σS(t0​)​∪{snegative_feeling(1)​,ssoothing_sensation(1)​}.

• snegative_feeling(1)s_{\text{negative\_feeling}}^{(1)}snegative_feeling(1)​: Discomfort.

• ssoothing_sensation(1)s_{\text{soothing\_sensation}}^{(1)}ssoothing_sensation(1)​: Relief when soothed.

• Formation of emotional semantic units:

• Update:

Interaction 2: Smiling in Response to Parental Smiles

• Emotional Input: Visual of parent's smile (dparent_smiled_{\text{parent\_smile}}dparent_smile​), leading to own smiling (dself_smiled_{\text{self\_smile}}dself_smile​).

• State Change in Semantic Space (ΔσS(t2)\Delta \sigma_S^{(t_2)}ΔσS(t2​)​):

• σS(t2)=σS(t1)∪{spositive_feeling(1),sfacial_expression(1)}\sigma_S^{(t_2)} = \sigma_S^{(t_1)} \cup \{ s_{\text{positive\_feeling}}^{(1)}, s_{\text{facial\_expression}}^{(1)} \}σS(t2​)​=σS(t1​)​∪{spositive_feeling(1)​,sfacial_expression(1)​}.

• spositive_feeling(1)s_{\text{positive\_feeling}}^{(1)}spositive_feeling(1)​: Pleasure.

• sfacial_expression(1)s_{\text{facial\_expression}}^{(1)}sfacial_expression(1)​: Smiling.

• Formation of:

• Update:

Conceptual Space Changes:

• At this stage, no significant emotional concepts are formed; σC(t2)=σC(t0)\sigma_C^{(t_2)} = \sigma_C^{(t_0)}σC(t2​)​=σC(t0​)​.

Cognitive Space Integration:

• The cognitive space now includes basic emotional semantic units but lacks structured emotional concepts.

4.2 Stage 2: Recognition of Others' Emotions (7-12 Months)4.2.1 Cognitive State Evolution

• Accumulated Emotional Semantic Units:

• σS(t3)=σS(t2)∪{stone_of_voice(1),stone_of_voice(2)}\sigma_S^{(t_3)} = \sigma_S^{(t_2)} \cup \{ s_{\text{tone\_of\_voice}}^{(1)}, s_{\text{tone\_of\_voice}}^{(2)} \}σS(t3​)​=σS(t2​)​∪{stone_of_voice(1)​,stone_of_voice(2)​}.

• stone_of_voice(1)s_{\text{tone\_of\_voice}}^{(1)}stone_of_voice(1)​: Happy tone.

• stone_of_voice(2)s_{\text{tone\_of\_voice}}^{(2)}stone_of_voice(2)​: Stern tone.

• State of Semantic Space (σS(t3)\sigma_S^{(t_3)}σS(t3​)​):

4.2.2 State Changes per Interaction

Interaction 3: Responding to Happy Tone

• Emotional Input: Parent speaks in a happy tone (dhappy_voiced_{\text{happy\_voice}}dhappy_voice​), leading to Emma's excitement.

• State Change in Semantic Space:

• Strengthening of spositive_feeling(1)s_{\text{positive\_feeling}}^{(1)}spositive_feeling(1)​ and stone_of_voice(1)s_{\text{tone\_of\_voice}}^{(1)}stone_of_voice(1)​.

• Concept Formation:

• chappiness=fC({spositive_feeling(1),sfacial_expression(1),stone_of_voice(1)})c_{\text{happiness}} = f_C(\{ s_{\text{positive\_feeling}}^{(1)}, s_{\text{facial\_expression}}^{(1)}, s_{\text{tone\_of\_voice}}^{(1)} \})chappiness​=fC​({spositive_feeling(1)​,sfacial_expression(1)​,stone_of_voice(1)​}).

• State Change in Conceptual Space (ΔσC(t4)\Delta \sigma_C^{(t_4)}ΔσC(t4​)​):

• σC(t4)=σC(t3)∪{chappiness}\sigma_C^{(t_4)} = \sigma_C^{(t_3)} \cup \{ c_{\text{happiness}} \}σC(t4​)​=σC(t3​)​∪{chappiness​}.

Interaction 4: Reacting to Stern Voice

• Emotional Input: Parent uses a stern tone (dstern_voiced_{\text{stern\_voice}}dstern_voice​) to indicate disapproval.

• State Change in Semantic Space:

• σS(t5)=σS(t4)∪{snegative_feeling(2)}\sigma_S^{(t_5)} = \sigma_S^{(t_4)} \cup \{ s_{\text{negative\_feeling}}^{(2)} \}σS(t5​)​=σS(t4​)​∪{snegative_feeling(2)​}.

• Formation of snegative_feeling(2)s_{\text{negative\_feeling}}^{(2)}snegative_feeling(2)​: Unease.

• Update:

• Concept Formation:

• cdiscomfort=fC({snegative_feeling(2),stone_of_voice(2)})c_{\text{discomfort}} = f_C(\{ s_{\text{negative\_feeling}}^{(2)}, s_{\text{tone\_of\_voice}}^{(2)} \})cdiscomfort​=fC​({snegative_feeling(2)​,stone_of_voice(2)​}).

• Update:

• σC(t5)=σC(t4)∪{cdiscomfort}\sigma_C^{(t_5)} = \sigma_C^{(t_4)} \cup \{ c_{\text{discomfort}} \}σC(t5​)​=σC(t4​)​∪{cdiscomfort​}.

Cognitive Space Integration:

• Cognitive space now includes basic emotional concepts associated with happiness and discomfort, enabling Emma to recognize others' emotions.

4.3 Stage 3: Expression and Regulation of Emotions (13-18 Months)4.3.1 Cognitive State Expansion

• New Emotional Semantic Units:

• sfrustration(1)s_{\text{frustration}}^{(1)}sfrustration(1)​: When unable to reach a toy.

• scomfort(1)s_{\text{comfort}}^{(1)}scomfort(1)​: When consoled after falling.

• State of Semantic Space (σS(t6)\sigma_S^{(t_6)}σS(t6​)​):

• σS(t6)=σS(t5)∪{sfrustration(1),scomfort(1)}\sigma_S^{(t_6)} = \sigma_S^{(t_5)} \cup \{ s_{\text{frustration}}^{(1)}, s_{\text{comfort}}^{(1)} \}σS(t6​)​=σS(t5​)​∪{sfrustration(1)​,scomfort(1)​}.

4.3.2 State Changes per Interaction

Interaction 5: Experiencing Frustration

• Action: Emma tries to reach a toy but can't.

• Emotional Input: Feels frustration (dfrustrationd_{\text{frustration}}dfrustration​) and cries.

• State Change in Semantic Space:

• Strengthening of sfrustration(1)s_{\text{frustration}}^{(1)}sfrustration(1)​.

• Concept Formation:

• cfrustration=fC({snegative_feeling(1),sfrustration(1)})c_{\text{frustration}} = f_C(\{ s_{\text{negative\_feeling}}^{(1)}, s_{\text{frustration}}^{(1)} \})cfrustration​=fC​({snegative_feeling(1)​,sfrustration(1)​}).

• Conceptual Space Update:

• σC(t7)=σC(t6)∪{cfrustration}\sigma_C^{(t_7)} = \sigma_C^{(t_6)} \cup \{ c_{\text{frustration}} \}σC(t7​)​=σC(t6​)​∪{cfrustration​}.

Interaction 6: Learning to Self-Soothe

• Action: Emma hugs a comfort object after being upset.

• State Change in Semantic Space:

• Formation of sself_soothing(1)s_{\text{self\_soothing}}^{(1)}sself_soothing(1)​: Relief from hugging toy.

• Concept Formation:

• cself_soothing=fC({scomfort(1),sself_soothing(1)})c_{\text{self\_soothing}} = f_C(\{ s_{\text{comfort}}^{(1)}, s_{\text{self\_soothing}}^{(1)} \})cself_soothing​=fC​({scomfort(1)​,sself_soothing(1)​}).

• Update:

• σC(t8)=σC(t7)∪{cself_soothing}\sigma_C^{(t_8)} = \sigma_C^{(t_7)} \cup \{ c_{\text{self\_soothing}} \}σC(t8​)​=σC(t7​)​∪{cself_soothing​}.

Cognitive Space Integration:

• Cognitive space now includes more complex emotional concepts, allowing Emma to not only recognize but also begin to regulate her emotions.

5. Mathematical Modeling of State Changes in Emotion Learning5.1 Semantic Space Transformations

• Addition of Emotional Semantic Units:

• σS(t+1)=σS(t)∪{snew}\sigma_S^{(t+1)} = \sigma_S^{(t)} \cup \{ s_{\text{new}} \}σS(t+1)​=σS(t)​∪{snew​}.

• Strengthening Units:

• si(t+1)=si(t)+Δss_i^{(t+1)} = s_i^{(t)} + \Delta ssi(t+1)​=si(t)​+Δs, where $\Delta s$ is proportional to emotional intensity.

• Example:

• sfrustration(1)(t+1)=sfrustration(1)(t)+Δss_{\text{frustration}}^{(1)(t+1)} = s_{\text{frustration}}^{(1)(t)} + \Delta ssfrustration(1)(t+1)​=sfrustration(1)(t)​+Δs.

5.2 Conceptual Space Transformations

• Formation of Emotional Concepts:

• ck=fC({si1,si2,...,sin})c_k = f_C(\{ s_{i_1}, s_{i_2}, ..., s_{i_n} \})ck​=fC​({si1​​,si2​​,...,sin​​}).

• Updating Concepts:

• ck(t+1)=ck(t)+γ∑(si−ck(t))c_k^{(t+1)} = c_k^{(t)} + \gamma \sum (s_i - c_k^{(t)})ck(t+1)​=ck(t)​+γ∑(si​−ck(t)​).

• Associations Between Concepts:

• Establishing links, e.g., chappiness↔csmilingc_{\text{happiness}} \leftrightarrow c_{\text{smiling}}chappiness​↔csmiling​.

5.3 Cognitive Space Integration

• Integration Function:

• C(t+1)=C(t)+ΔσS(t+1)+ΔσC(t+1)\mathcal{C}^{(t+1)} = \mathcal{C}^{(t)} + \Delta \sigma_S^{(t+1)} + \Delta \sigma_C^{(t+1)}C(t+1)=C(t)+ΔσS(t+1)​+ΔσC(t+1)​.

• State Changes:

• Reflect cumulative changes influenced by emotional experiences.

6. Visualization of State Changes6.1 Diagrams of Cognitive Spaces

• Semantic Space Maps:

• Nodes represent emotional semantic units.

• Edges indicate relationships like similarity or co-occurrence.

• Conceptual Space Maps:

• Clusters represent emotional concepts.

• Links show associations between concepts.

6.2 Graphical Representation of Transformations

• Time-Series Graphs:

• Display the development of semantic units and concepts over time.

• State Transition Diagrams:

• Highlight key interactions leading to state changes.

7. Discussion7.1 Insights from Detailed State Changes

• Emotions as Integral to Cognitive Development:

• Emotional experiences significantly influence the formation of semantic units and concepts.

• Social Interaction's Role:

• Interactions with caregivers are crucial for recognizing and interpreting emotions.

• Self-Regulation Emergence:

• The development of concepts like self-soothing indicates the beginning of emotional regulation.

7.2 Implications for AI and Cognitive Science

• Modeling Emotional Intelligence:

• AI systems can incorporate emotional learning models to improve human-computer interaction.

• Adaptive Systems:

• Emotionally aware AI can adjust responses based on user emotions.

• Cognitive Development Studies:

• Provides a framework for understanding how emotions influence cognitive processes.

7.3 Limitations and Future Directions

• Complexity of Emotions:

• Emotions are multifaceted and influenced by numerous factors not fully captured here.

• Cultural Variations:

• Emotional expression and interpretation can vary widely across cultures.

• Further Research:

• Integrating more nuanced emotional states and social contexts into the model.

8. Conclusion

This detailed simulation illustrates the significant role of emotion learning in shaping an infant's cognitive, semantic, and conceptual spaces. By modeling the state changes using the DIKWP Semantic Mathematics framework, we observe how emotional experiences lead to the formation and reinforcement of semantic units and concepts, contributing to overall cognitive and social development. This approach enhances our understanding of human cognition and offers valuable insights for developing emotionally intelligent AI systems.

9. References

1. International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation (DIKWP-SC),World Association of Artificial Consciousness(WAC),World Conference on Artificial Consciousness(WCAC). Standardization of DIKWP Semantic Mathematics of International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP ) Model. October 2024 DOI: 10.13140/RG.2.2.26233.89445 .  https://www.researchgate.net/publication/384637381_Standardization_of_DIKWP_Semantic_Mathematics_of_International_Test_and_Evaluation_Standards_for_Artificial_Intelligence_based_on_Networked_Data-Information-Knowledge-Wisdom-Purpose_DIKWP_Model

2. 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. ".

3. Izard, C. E. (1994). Innate and Universal Facial Expressions: Evidence from Developmental and Cross-Cultural Research. Psychological Bulletin, 115(2), 288-299.

4. Campos, J. J., & Stenberg, C. (1981). Perception, Appraisal, and Emotion: The Onset of Social Referencing. In M. Lamb & L. Sherrod (Eds.), Infant Social Cognition.

5. Saarni, C., & Harris, P. L. (1989). Children's Understanding of Emotion. Cambridge University Press.

6. Gärdenfors, P. (2000). Conceptual Spaces: The Geometry of Thought. MIT Press.

7. Gross, J. J. (2014). Emotion Regulation: Conceptual and Empirical Foundations. In J. J. Gross (Ed.), Handbook of Emotion Regulation.

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

9. Barrett, L. F. (2017). How Emotions Are Made: The Secret Life of the Brain. Houghton Mifflin Harcourt.

Keywords: DIKWP Semantic Mathematics, Cognitive State Changes, Semantic Space, Conceptual Space, Infant Emotion Learning, Cognitive Development, Prof. Yucong Duan, Cognitive Modeling, Artificial Intelligence, Emotional Intelligence, Semantic Integration, Concept Formation, Social Development.