# POMDP Structure Guide

## Overview
This guide explains our modular approach to representing Active Inference POMDPs using Obsidian's knowledge management capabilities.

## Philosophy
Our approach combines:
1. Machine-readable matrix specifications
2. Human-readable documentation
3. Bidirectional linking for relationships
4. Version control for evolution
5. Visualization capabilities

## Core Components

### Matrix Specifications
Each POMDP matrix has its own specification:
- [[A_matrix]] - Perception (observation mapping)
- [[B_matrix]] - Transitions (dynamics)
- [[C_matrix]] - Preferences (goals)
- [[D_matrix]] - Priors (initial beliefs)
- [[E_matrix]] - Affordances (policies)

### State Spaces
Fundamental spaces are defined separately:
- [[o_space]] - Observation space
- [[s_space]] - Hidden state space
- [[pi_space]] - Policy space

## Machine Readability

### YAML Frontmatter
```yaml
---
type: matrix_spec
id: unique_identifier
matrix_type: perception
created: timestamp
modified: timestamp
tags: [matrix, type, active-inference]
related_spaces: [space1, space2]
---
```

### Matrix Data Structure
```yaml
matrix_data:
  format: numpy.ndarray
  dtype: float32
  initialization: method
  storage: path/to/data.npy
```

### Constraints
```yaml
constraints:
  - mathematical_property
  - dimensional_requirement
  - probability_constraint
```

## Knowledge Integration

### Bidirectional Links
- Matrix ↔ Space relationships
- Component dependencies
- Implementation references

### Tag Taxonomy
- #matrix
- #state-space
- #active-inference
- #pomdp
- #generative-model

## Computational Interface

### Matrix Operations
```python
from src.models.matrices import MatrixLoader

# Load matrix specification
A = MatrixLoader.load("A_matrix")

# Perform operations
result = A.update(observation)
```

### State Space Interface
```python
from src.models.spaces import StateSpace

# Initialize space
s_space = StateSpace.from_spec("s_space")

# Update beliefs
s_space.update_belief(evidence)
```

## Visualization Pipeline

### Matrix Visualization
1. Load specification from markdown
2. Read matrix data
3. Generate visualization
4. Export to desired format

### Network Visualization
1. Extract relationship graph
2. Apply layout algorithm
3. Render interactive view
4. Enable exploration

## Version Control

### Matrix Evolution
- Track changes in specifications
- Version matrix data
- Document modifications
- Maintain history

### Knowledge Base Updates
- Link updates
- Relationship changes
- Documentation evolution
- Implementation refinements

## Integration Examples

### Active Inference Implementation
```python
class ActiveInferencePOMDP:
    def __init__(self, agent_spec: str):
        self.A = MatrixLoader.load("A_matrix")
        self.B = MatrixLoader.load("B_matrix")
        self.C = MatrixLoader.load("C_matrix")
        self.D = MatrixLoader.load("D_matrix")
        self.E = MatrixLoader.load("E_matrix")
        
    def infer_state(self, observation):
        """Perform state inference"""
        pass
    
    def select_policy(self):
        """Select optimal policy"""
        pass
```

### Visualization Generation
```python
class POMDPVisualizer:
    def __init__(self, agent_spec: str):
        self.spec = load_spec(agent_spec)
        
    def plot_matrices(self):
        """Generate matrix plots"""
        pass
    
    def plot_state_space(self):
        """Visualize state space"""
        pass
```

## Best Practices

### Specification Writing
1. Clear structure
2. Complete metadata
3. Explicit constraints
4. Comprehensive documentation

### Knowledge Organization
1. Consistent naming
2. Meaningful links
3. Proper tagging
4. Regular updates

### Implementation
1. Type checking
2. Constraint validation
3. Error handling
4. Performance optimization

## Related Guides
- [[matrix_operations]]
- [[visualization_guide]]
- [[implementation_guide]]
- [[version_control]]

## References
- [[active_inference_theory]]
- [[pomdp_formalism]]
- [[obsidian_usage]]
- [[git_workflow]]