MCP-Logic

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# WorkflowDetails

## Purpose and Overview

The workflow details document provides a comprehensive guide for using and maintaining the MCP Logic server. This system serves as a bridge between formal logical reasoning and modern AI systems, enabling:

1. Automated theorem proving
2. Counterexample generation
3. Integration with knowledge bases
4. Formal verification of AI reasoning

This document outlines the key workflows for effectively utilizing these capabilities while maintaining system integrity and performance.

## Step-by-Step Explanations

### 1. Server Setup and Configuration
1. Install Dependencies:
   ```bash
   pip install mcp-logic
   ```

2. Configure Environment:
   - Set Prover9-Mace4 binary path
   - Configure logging
   - Set up integration points

3. Start Server:
   ```bash
   uv run mcp_logic --prover-path /path/to/Prover9-Mace4/bin
   ```

### 2. Proof Workflow
1. Prepare Logical Statements:
   ```python
   premises = [
       "all x (P(x) -> Q(x))",
       "P(a)"
   ]
   conclusion = "Q(a)"
   ```

2. Submit Proof Request:
   ```python
   result = prove(premises, conclusion)
   ```

3. Handle Results:
   - Check for success/failure
   - Analyze proof steps
   - Process counterexamples

### 3. Integration Workflow
1. Knowledge Base Integration:
   - Store proven theorems
   - Track proof dependencies
   - Maintain lemma libraries

2. AI System Integration:
   - Verify AI reasoning
   - Generate formal proofs
   - Provide counterexamples

## Annotated Examples

### 1. Basic Proof Example
```python
# Simple modus ponens proof
from mcp_logic import prove

result = prove(
    premises=[
        "P -> Q",  # If P then Q
        "P"        # P is true
    ],
    conclusion="Q"  # Therefore Q
)

if result.success:
    print("Proof found:", result.steps)
else:
    print("Checking for counterexample...")
    model = find_counterexample(premises, conclusion)
```

### 2. Modal Logic Example
```python
# Proving necessity distributes over implication
result = prove(
    premises=["box(P -> Q)"],
    conclusion="box(P) -> box(Q)",
    logic_type="modal"
)
```

### 3. Knowledge Base Integration
```python
# Store a proven theorem in neo4j
neo4j.execute_query("""
    CREATE (t:Theorem {
        name: 'modus_ponens',
        premises: ['P -> Q', 'P'],
        conclusion: 'Q',
        proof_steps: $steps
    })
""", {'steps': result.steps})
```

### 4. Multi-Agent Reasoning
```python
# Proving knowledge transfer between agents
result = prove(
    premises=[
        "knows(a, knows(b, P))",     # Agent a knows that b knows P
        "all x (knows(x,P) -> P)"    # Knowledge implies truth
    ],
    conclusion="P"
)
```

### 5. Error Handling Example
```python
try:
    result = prove(premises, conclusion, timeout=30)
except SyntaxError as e:
    print("Invalid logical syntax:", e)
except TimeoutError:
    print("Proof search exceeded time limit")
    model = find_counterexample(premises, conclusion)
```
[Code snippets, diagrams, or flowcharts for clarity]

## Contextual Notes

### Historical Context
1. Development Motivation:
   - Need for formal verification in AI systems
   - Integration of classical logic with modern AI
   - Support for distributed reasoning systems

2. Design Evolution:
   - Started with basic first-order logic
   - Added modal logic support
   - Integrated with knowledge bases
   - Enhanced multi-agent capabilities

### Current Status
1. Core Features:
   - First-order logic proving
   - Modal logic support
   - Multi-agent reasoning
   - Counterexample generation

2. Integration Points:
   - Neo4j knowledge base
   - MCP framework
   - AI reasoning systems
   - Documentation system

### Future Directions
1. Planned Enhancements:
   - Extended modal logic operators
   - Temporal logic support
   - Improved proof visualization
   - Enhanced counterexample analysis

2. Research Areas:
   - AI knowledge verification
   - Distributed theorem proving
   - Automated proof strategies
   - Knowledge consistency checking
[Historical decisions, trade-offs, and anticipated challenges]

## Actionable Advice

### Best Practices
1. Proof Development:
   - Start with simplified versions of complex proofs
   - Build up complexity gradually
   - Document all assumptions clearly
   - Keep premises minimal
   - Use established patterns where possible

2. Error Prevention:
   - Validate syntax before submission
   - Check operator precedence carefully
   - Use parentheses liberally for clarity
   - Test with known theorems first
   - Document failed proof attempts

3. Performance Optimization:
   - Set appropriate timeouts
   - Break complex proofs into lemmas
   - Cache frequently used results
   - Monitor proof search patterns
   - Use counterexamples early

### Common Pitfalls
1. Syntax Issues:
   - Mismatched parentheses
   - Incorrect operator precedence
   - Undefined variables
   - Invalid modal operators
   - Improper quantifier placement

2. Logic Errors:
   - Circular reasoning
   - Missing premises
   - Overcomplex formulations
   - Implicit assumptions
   - Inconsistent definitions

3. Integration Problems:
   - Database connection timing
   - Transaction management
   - Memory management
   - Timeout handling
   - Error propagation

### Maintenance Tips
1. Regular Tasks:
   - Update operator libraries
   - Check integration points
   - Verify example proofs
   - Update documentation
   - Monitor system logs

2. Troubleshooting:
   - Check syntax first
   - Validate premises
   - Test with simpler cases
   - Review proof strategy
   - Examine counterexamples
[Gotchas, edge cases, and common pitfalls to avoid]