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Project 3: Formal Methods & Causal Inference

Elevating CNS 2.0's reasoning capabilities by integrating formal logical systems and causal reasoning frameworks.

The Challenge: From Plausibility to Provability

The core CNS 2.0 system, even with a GNN-based logic critic, operates primarily in the realm of plausibility. It generates syntheses that are coherent, well-grounded, and structurally sound based on patterns learned from data. However, it cannot formally prove that its conclusions are logically valid, nor can it distinguish a robust causal link from a simple correlation. For high-stakes domains like mathematical proofs, legal reasoning, or scientific discovery, this is a critical limitation.

The Vision: A System that Reasons with Rigor

This research project aims to bridge the gap between pattern-based natural language reasoning and rigorous, formal systems of logic and causality. The goal is to create a version of CNS 2.0 that can not only generate plausible narratives but also validate them using formal methods and explicitly model the causal relationships within them, transforming it into an engine for rigorous knowledge synthesis.

Key Research Questions

  1. The Language-to-Logic Bridge: How can we create a reliable “bridge” to translate the natural language claims and relationships in a reasoning graph into a formal language (e.g., predicate logic, temporal logic)?
  2. Formal Verification: Can we use automated theorem provers or model checkers to formally verify the logical consistency of a generated synthesis, providing a binary pass/fail signal for logical validity?
  3. Correlation vs. Causation: How can we enhance the reasoning graph to distinguish between correlational links (“supports”) and precise causal relationships (e.g., “causes,” “prevents,” “is a necessary condition for”)?
  4. Causal Discovery: Can we integrate causal discovery algorithms (like Do-calculus or the PC algorithm) to analyze the evidence set and propose or validate a causal graph structure?
  5. Reasoning Under Uncertainty: How can we best represent and reason with different types of uncertainty (e.g., randomness vs. lack of knowledge) using advanced frameworks like probabilistic logic programming or modal logic?

Proposed Methodology

This project combines deep theoretical work with practical implementation, divided into two parallel thrusts.

Part 1: Formal Methods Integration

This part focuses on integrating the rigor of formal logic into the critic pipeline.

  • Semantic Parsing to Formal Logic: We will develop and fine-tune models for semantic parsing, specifically designed to translate the natural language claims and relations from a SNO’s Reasoning Graph into a formal, symbolic representation like First-Order Logic or Temporal Logic.
  • Automated Theorem Prover Integration: We will build a pipeline that feeds this formal representation into an off-the-shelf automated theorem prover (e.g., Z3, Vampire). The prover will be tasked with checking the internal consistency of the argument and verifying that the synthesized hypothesis logically follows from the provided premises and evidence.
  • A New Critic: FormalValidityScore: The output of the theorem prover will be used to create a new, powerful signal in the CriticPipeline: a FormalValidityScore. This score, potentially binary (provably valid / not valid) or graded, would provide the system’s most rigorous assessment of logical soundness.

Part 2: Causal Reasoning Enhancement

This part focuses on moving beyond correlation to causation.

  • Causal Graph Representation: We will enhance the reasoning graph G to support explicitly causal edge types, drawing from the Pearlian school of causality. This will allow SNOs to represent precise causal claims.
  • A New Critic: CausalCritic: We will develop a new critic component dedicated to assessing the validity of these causal claims. The CausalCritic will:
    1. Use causal discovery algorithms (e.g., PC, FCI) to analyze the data in the EvidenceSet to determine if the claimed causal link is statistically supported.
    2. Employ principles from frameworks like Judea Pearl’s Do-calculus to reason about the effects of interventions and counterfactuals, providing a deeper level of causal understanding.
  • Causal Synthesis Engine: The GenerativeSynthesisEngine will be updated with new, structured prompts designed to encourage the generation of explicit and testable causal hypotheses, rather than just descriptive or correlational ones.

Expected Contribution

Successfully integrating formal methods and causal inference would represent a monumental leap in the reasoning capabilities of AI systems. It would move CNS 2.0 from a system that synthesizes plausible narratives to one that synthesizes rigorous knowledge. This research could have profound implications for fields like law (verifying legal arguments), science (accelerating discovery by validating causal hypotheses), and mathematics (assisting in the generation and verification of proofs), enabling a new class of AI-powered tools for discovery, verification, and understanding.