MCP-Logic

# IntegrationGuides ## Purpose and Overview The MCP Logic server is designed to integrate with various AI and knowledge management systems. This guide covers integration patterns, best practices, and common use cases for: 1. AI System Integration: - Formal verification of AI reasoning - Knowledge consistency checking - Automated theorem proving support - Logical inference capabilities 2. Knowledge Base Integration: - Theorem storage and retrieval - Proof history tracking - Dependency management - Pattern recognition 3. Development Integration: - API usage patterns - Error handling - Resource management - Performance optimization This guide provides concrete examples and implementation patterns for each integration scenario. [Why this domain is critical to the project] ## Step-by-Step Explanations ### AI System Integration 1. Setting Up MCP Client: ```python from mcp.client import Client async def setup_logic_client(): client = Client() await client.connect("mcp-logic") return client ``` 2. Implementing Verification: ```python class AIVerifier: def __init__(self, mcp_client: Client): self.client = mcp_client async def verify_reasoning( self, premises: list[str], conclusion: str ) -> bool: response = await self.client.call_tool( "prove", { "premises": premises, "conclusion": conclusion } ) return response[0].success ``` 3. Knowledge Consistency: ```python async def check_consistency(knowledge_base: list[str]) -> bool: # Check that knowledge base doesn't imply a contradiction result = await prove( premises=knowledge_base, conclusion="P & -P" ) return not result.success ``` ### Knowledge Base Integration 1. Neo4j Setup: ```python from neo4j import GraphDatabase class TheoremStore: def __init__(self, uri: str): self.driver = GraphDatabase.driver(uri) async def store_theorem(self, theorem: Theorem): await self.driver.execute_query(""" MERGE (t:Theorem { name: $name, premises: $premises, conclusion: $conclusion }) """, theorem.__dict__) ``` 2. Proof History: ```python async def track_proof_history(proof: ProofResult): await neo4j.execute_query(""" MATCH (t:Theorem {name: $name}) CREATE (p:Proof { timestamp: datetime(), steps: $steps, success: $success }) CREATE (t)-[:HAS_PROOF]->(p) """, { "name": proof.theorem_name, "steps": proof.steps, "success": proof.success }) ``` 3. Pattern Recognition: ```python async def find_similar_theorems(theorem: Theorem): return await neo4j.execute_query(""" MATCH (t:Theorem) WHERE any(p IN t.premises WHERE p IN $premises) AND t.conclusion = $conclusion RETURN t """, { "premises": theorem.premises, "conclusion": theorem.conclusion }) ``` ### Development Integration 1. Error Handling: ```python class LogicIntegration: async def safe_prove( self, premises: list[str], conclusion: str ) -> ProofResult: try: return await self.client.call_tool( "prove", { "premises": premises, "conclusion": conclusion } ) except Exception as e: logger.error(f"Proof error: {e}") return ProofResult( success=False, error=str(e) ) ``` 2. Resource Management: ```python class ProofManager: def __init__(self, max_concurrent: int = 4): self.semaphore = asyncio.Semaphore(max_concurrent) self.active_proofs = set() async def prove(self, *args, **kwargs): async with self.semaphore: proof_id = str(uuid.uuid4()) self.active_proofs.add(proof_id) try: return await self.client.prove(*args, **kwargs) finally: self.active_proofs.remove(proof_id) ``` 3. Performance Monitoring: ```python class PerformanceMonitor: def __init__(self): self.metrics = defaultdict(list) async def track_operation( 'prove', self.prover.prove( premises, conclusion, timeout=t ) ) if result.success: # Cache successful proof self.cache[cache_key] = result return result elif result.has_counterexample: # Cache counterexample self.cache[cache_key] = result return result return ProofResult( success=False, reason="timeout_exhausted" ) def make_cache_key( self, premises: List[str], conclusion: str ) -> str: # Create stable cache key sorted_premises = sorted(premises) return f"{','.join(sorted_premises)}|{conclusion}" ``` ### 4. Modal Logic Integration Example ```python class ModalLogicVerifier: def __init__(self, mcp_client: Client): self.client = mcp_client self.known_operators = { 'box': 'necessity', 'dia': 'possibility', 'knows': 'knowledge' } async def verify_modal_statement( self, modal_premises: List[str], modal_conclusion: str, logic_type: str = 'S4' # Default to S4 modal logic ) -> ProofResult: # Add modal logic axioms based on type axioms = self.get_modal_axioms(logic_type) all_premises = axioms + modal_premises return await self.client.call_tool( "prove", { "premises": all_premises, "conclusion": modal_conclusion, "logic_type": "modal" } ) def get_modal_axioms(self, logic_type: str) -> List[str]: # Basic modal logic axioms axioms = [ "all x (box(x) -> -dia(-x))", # Duality of box/diamond "all x y (box(x -> y) -> (box(x) -> box(y)))" # K axiom ] if logic_type == 'S4': # Add S4 specific axioms axioms.extend([ "all x (box(x) -> x)", # T axiom "all x (box(x) -> box(box(x)))" # 4 axiom ]) elif logic_type == 'S5': # Add S5 specific axioms axioms.extend([ "all x (box(x) -> x)", # T axiom "all x (-box(x) -> box(-box(x)))" # 5 axiom ]) return axioms ``` ## Contextual Notes ### Integration Design Patterns 1. Service Layer Pattern: - Separate MCP interface from business logic - Handle connection lifecycle - Manage resources efficiently - Provide clean error handling 2. Repository Pattern: - Abstract theorem storage - Handle data persistence - Manage proof history - Enable pattern analysis 3. Event-Driven Integration: - React to proof completion - Track system metrics - Handle timeouts gracefully - Maintain audit logs ### Performance Considerations 1. Caching Strategy: - Cache proven theorems - Store counterexamples - Index common patterns - Manage cache invalidation 2. Resource Management: - Control concurrent proofs - Monitor memory usage - Handle long-running proofs - Clean up resources 3. Error Recovery: - Graceful degradation - Retry mechanisms - Circuit breakers - Fallback strategies ## Actionable Advice ### Best Practices 1. Connection Management: - Use connection pools - Implement timeouts - Handle reconnection - Clean up resources 2. Error Handling: - Define error types - Provide context - Log appropriately - Recover gracefully 3. Testing: - Unit test integration points - Simulate failures - Test timeout handling - Verify resource cleanup ### Common Pitfalls 1. Integration Issues: - Unhandled connection errors - Resource leaks - Missing timeouts - Incorrect error handling 2. Performance Problems: - Unbounded caches - Resource exhaustion - Blocking operations - Memory leaks 3. Maintenance Challenges: - Poor monitoring - Inadequate logging - Missing documentation - Unclear error messages ### Troubleshooting Guide 1. Connection Issues: ```python async def diagnose_connection(): try: # Check MCP connection await client.ping() # Verify Prover9 access await prover.test_connection() # Test database access await storage.ping() except Exception as e: logger.error(f"Connection error: {e}") return False return True ``` 2. Performance Issues: ```python async def check_performance(): metrics = await collect_metrics() # Check proof times if metrics.avg_proof_time > 5.0: logger.warning("High average proof time") # Monitor memory if metrics.memory_usage > 80: logger.warning("High memory usage") # Track success rate if metrics.proof_success_rate < 0.9: logger.warning("Low proof success rate") ``` 3. Resource Monitoring: ```python class ResourceMonitor: def __init__(self): self.active_connections = set() self.proof_attempts = 0 self.memory_usage = [] async def monitor(self): while True: stats = { "connections": len(self.active_connections), "proofs": self.proof_attempts, "memory": sum(self.memory_usage) / len(self.memory_usage) } await log_metrics(stats) await asyncio.sleep(60) ``` self, operation_name: str, coroutine: Awaitable[T] ) -> T: start_time = time.time() try: result = await coroutine duration = time.time() - start_time self.metrics[operation_name].append({ "duration": duration, "success": True }) return result except Exception as e: duration = time.time() - start_time self.metrics[operation_name].append({ "duration": duration, "success": False, "error": str(e) }) raise ``` [Concrete, detailed steps for implementation and maintenance] ## Annotated Examples [Code snippets, diagrams, or flowcharts for clarity] ## Contextual Notes [Historical decisions, trade-offs, and anticipated challenges] ## Actionable Advice [Gotchas, edge cases, and common pitfalls to avoid]