MCP-Logic

Rough Integration Plan for Reactive Agent Architecture /home/ty/Repositories/ai_workspace/reflective-agent-architecture Synthesis: Three-Phase Implementation Roadmap Based on the successful hypotheses (DiscoRL ↔ categorical functors, PyZX ↔ Neo4j formalization bridge) and your existing infrastructure: Phase 1: PyZX Foundation (Weekend - Proof of Concept) Goal: Demonstrate categorical diagrammatic reasoning works and connects to your needs bashcd /home/ty/Repositories/ai_workspace mkdir categorical-reasoning-bridge cd categorical-reasoning-bridge uv venv && source .venv/bin/activate uv pip install pyzx numpy networkx neo4j Critical First Script (proof_of_concept.py): python""" Demonstration: ZX-calculus as working example of categorical diagrammatic reasoning that you can actually run and verify. """ import pyzx as zx # Generate quantum circuit (morphism in dagger compact category) circuit = zx.generate.cliffordT(5, 50) print(f"Original: {circuit.stats()}") # Apply categorical rewrite rules (diagram chasing) zx.simplify.full_reduce(circuit) print(f"Simplified: {circuit.stats()}") # This demonstrates: # 1. Visual diagrams as rigorous math objects # 2. Sound rewrite rules (provably correct transformations) # 3. Automated verification (the simplification preserves equivalence) Why this matters: PyZX proves the entire pipeline works. It's not theoretical - it's a production system for quantum computing that does exactly what your documents propose: formal categorical reasoning on visual diagrams with automated verification. Phase 2: Neo4j Bridge (Week 2 - Practical Integration) Goal: Connect categorical formalism to your existing knowledge graphs Create neo4j_categorical_bridge.py: python""" Bridge: Treat Neo4j knowledge graphs as pre-categorical structures that can be formalized using categorical composition rules. """ from neo4j import GraphDatabase import pyzx as zx import networkx as nx class CategoricalKnowledgeGraph: """ Treats Neo4j graphs as objects in a category where: - Nodes → Objects - Edges → Morphisms - Paths → Composed morphisms """ def __init__(self, uri, user, password): self.driver = GraphDatabase.driver(uri, auth=(user, password)) def extract_reasoning_pattern(self, cypher_query): """ Extract graph pattern from Cypher query. This pattern is a "diagram" we want to formalize/verify. """ with self.driver.session() as session: result = session.run(cypher_query) return self._graph_to_categorical_repr(result) def _graph_to_categorical_repr(self, result): """ Convert Neo4j graph to categorical structure. This is the KEY TRANSLATION: Neo4j pattern → Morphisms in monoidal category """ # Build networkx graph from Neo4j result nx_graph = nx.DiGraph() for record in result: # Extract nodes and relationships # Add to nx_graph pass return nx_graph def verify_commutativity(self, pattern_a, pattern_b): """ Verify if two reasoning patterns are equivalent. This is the "commerge problem" from Document 1: Do different paths through the diagram commute? For simple cases, check if paths yield same result. For complex cases, would delegate to Prover9. """ # Check structural equivalence return self._check_graph_isomorphism(pattern_a, pattern_b) What this achieves: Your Neo4j reasoning patterns (emotional state transitions, cognitive architecture flows) can now be analyzed for formal properties: Are two reasoning paths equivalent? Does a transformation preserve semantic meaning? Can we prove a property holds across all valid paths? Phase 3: Prover9 Verification (Weeks 3-4 - Formal Guarantees) Goal: Close the loop with automated theorem proving Create formal_verification_pipeline.py: python""" Complete pipeline: Neo4j → Categorical → First-Order Logic → Prover9 """ import subprocess import tempfile class CategoryTheoryToFOL: """ Translate categorical diagram properties to FOL statements that Prover9 can verify. """ def diagram_to_fol(self, diagram, property_claim): """ Convert diagram commutativity claim to FOL. Example: "Path A→B→C equals path A→C" becomes FOL: ∀x. (c(b(a(x))) = c(a(x))) """ fol_statements = [] # Extract composition structure paths = self._extract_paths(diagram) for path in paths: # Convert path to function composition composed = self._compose_morphisms(path) fol_statements.append(composed) # Add equality claim for commutativity if len(paths) == 2: fol_statements.append(f"equal({paths[0]}, {paths[1]}).") return "\n".join(fol_statements) def verify_with_prover9(self, fol_statements): """ Send to your existing mcp-logic server with Prover9. """ # Create Prover9 input file prover9_input = f""" formulas(assumptions). {fol_statements} end_of_list. formulas(goals). % Commutativity goal here end_of_list. """ # Write to temp file and call Prover9 with tempfile.NamedTemporaryFile(mode='w', suffix='.in') as f: f.write(prover9_input) f.flush() result = subprocess.run( ['prover9', '-f', f.name], capture_output=True, text=True ) return self._parse_prover9_output(result.stdout) Why This Matters to Your Work 1. Cognitive Architectures → Formally Verified Your cognitive-workspace-db reasoning patterns can be proven correct: python# Example: Verify emotional state transition logic kg = CategoricalKnowledgeGraph(neo4j_uri, user, pwd) # Extract reasoning pattern arousal_path = kg.extract_reasoning_pattern(""" MATCH (s1:EmotionalState {name: 'calm'})-[t1:TRANSITIONS_TO]-> (s2:EmotionalState {name: 'aroused'})-[t2:TRANSITIONS_TO]-> (s3:EmotionalState {name: 'stressed'}) RETURN s1, t1, s2, t2, s3 """) # Verify property: "Arousal always increases monotonically" verifier = CategoryTheoryToFOL() fol = verifier.diagram_to_fol(arousal_path, "monotonic_increase") proof = verifier.verify_with_prover9(fol) if proof.success: print("✓ Emotional transition logic is formally correct") else: print("✗ Found inconsistency:", proof.counterexample) 2. Graph of Thoughts → Provably Sound Your graph-of-thoughts reasoning system gets mathematical guarantees: Thought composition rules are categorical morphisms Reasoning chains are verified for logical consistency Novel connections are checked for validity before assertion 3. DiscoRL Connection (The Deep Insight) The Nature 2025 DiscoRL paper's meta-network that discovers RL algorithms is already doing categorical reasoning, just implicitly. Your formalization work could: Make discovered algorithms interpretable: Translate DiscoRL's neural update rules into categorical diagrams Verify correctness: Prove discovered algorithms satisfy formal properties Guide discovery: Use categorical constraints to bias the search toward provably correct algorithms Immediate Next Action Choose ONE: Option A (Fastest validation): bash# Install PyZX, run the 5-line proof-of-concept # See categorical diagrammatic reasoning work in 10 minutes Option B (Most relevant to existing work): bash# Create the Neo4j bridge # Pick ONE reasoning pattern from your cognitive architecture # Formalize it categorically and verify a property Option C (Most ambitious): bash# Full pipeline: Neo4j → PyZX → Prover9 # Verify an emotional state transition chain is formally consistent