Constrained Object Hierarchies (COH) provides a neuroscience-inspired theoretical framework for modeling Artificial General Intelligence (AGI). As a flexible and robust foundation, COH supports the representation of general intelligent systems across diverse domains.
Formally, a COH is defined as a 9-tuple:
O = (C, A, M, N, E, I, T, G, D)
Where:
- C: Components – sub-objects organized hierarchically
- A: Attributes – state variables describing object properties
- M: Methods – executable actions associated with components
- N: Neural Components – adaptive models for learning and inference
- E: Embedding Neural Component – semantic representation of the COH
- I: Identity Constraints – rules ensuring object integrity
- T: Trigger Constraints – event-condition-action rules for dynamic behavior
- G: Goal Constraints – optimization objectives guiding intelligent behavior
- D: Constraint Daemons – real-time monitors enforcing system constraints
Based on the COH framework, the modelling process and result of Adaptive Math Tutoring System are as follows:
Description & Significance: This system provides personalized instruction in mathematics by adapting the sequence and difficulty of problems based on a student's performance. It is significant for scaling individualized learning, a key challenge in education [6].
Analysis & Requirements: The system must maintain a model of student knowledge, select appropriate problems, assess responses, and provide feedback. Requirements include accurate knowledge assessment, effective problem sequencing, and adaptive hint provision.
COH Solution Design: The top-level object is the Tutor. Key components are StudentModel, ProblemSelector, and FeedbackEngine. Adaptation is handled by a knowledge tracing model (N). Goals (G) involve maximizing learning efficiency.
COH Modelling Solution:
- C:
StudentModel, ProblemSelector, FeedbackEngine, CurriculumGraph
- A:
student_proficiency_map, current_problem, session_time
- M:
select_next_problem(), assess_answer(), update_proficiency()
- N: A Bayesian Knowledge Tracing model within
StudentModel.
- E: Knowledge components embedded by prerequisite structure.
- I:
proficiency_score ∈ [0,1]; A problem must map to a knowledge component.
- T: ON
assess_answer(incorrect) IF hints_given < 3 DO generate_hint().
- G: Maximize the sum of
student_proficiency_map over time.
- D: Monitors for rapid successive failures to trigger an easier problem.
The COH model explicitly separates concerns (modelling, selection, feedback). The intelligence emerges from the BKT model (N) updating the state (A), which is used by the trigger (T) and goal (G) constraints to drive pedagogical decisions. The hierarchy allows for easy extension (e.g., adding a new component for gamification).
You may choose this topic and pursue one of the following routes:
📝 Essay
- Survey existing methodologies for modeling, designing, and implementing similar intelligent systems.
- Include:
- Literature synthesis
- COH framework analysis
- Critical evaluation of competing approaches
🛠️ Project
- Design and implement the system using the COH model.
- Include:
- System architecture and design
- Development and testing
- Demonstration of core functionality
🎓 Thesis
- Explore COH’s theoretical foundations in depth.
- Include:
- Proposed enhancements or extensions
- Implementation and evaluation
- Development of an advanced intelligent system grounded in COH principles
|
