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Project 1: GNNs for Logical Reasoning

Developing a next-generation, data-driven Logic Critic using Graph Neural Networks to assess the structural integrity of arguments.

The Challenge: Beyond Heuristics

The heuristic-based LogicCritic developed in the foundational phase (and implemented in Chapter 3 of the Developer’s Guide) is transparent and effective for well-structured arguments. However, it has significant limitations. It relies on a predefined set of rules and cannot easily detect more subtle or novel forms of logical fallacies, nor can it learn from new data. To truly assess the complex reasoning graphs that will be generated at scale, we need a more powerful, data-driven approach.

The Vision: A Self-Learning Logic Critic

This research project aims to replace the heuristic logic critic with a sophisticated Graph Neural Network (GNN) model. A GNN is the ideal architecture for this task because it is specifically designed to learn from graph-structured data. The GNN-based critic will learn to identify the subtle structural properties that differentiate a coherent, logical argument from a fallacious one, directly implementing the Score_L = f_GNN(G; θ) function defined in the CNS 2.0 Blueprint.

Key Research Questions

This research seeks to answer several fundamental questions about applying GNNs to formal reasoning:

  1. Efficacy: Can a GNN model be trained to effectively and consistently classify the logical soundness of complex, multi-step reasoning graphs?
  2. Architecture: What graph representations and GNN architectures (e.g., GCNs, GATs, or custom models) are best suited for capturing the directed, typed, and hierarchical nature of logical relationships? How can we best model the flow of inference?
  3. Data Curation: How can we create a large-scale, high-quality dataset of labeled reasoning graphs—including both valid arguments and a diverse range of fallacies—to train a robust and generalizable model?
  4. Explainability: How can we ensure the GNN’s reasoning is explainable? Can we use techniques like GNNExplainer to not only get a score but to highlight the specific premises or inferential steps that lead to a fallacious conclusion?
  5. Temporal Dynamics: Can we incorporate temporal graph network components to model how the validity of an argument evolves as new evidence becomes available over time?

Proposed Methodology

Drawing from the advanced concepts outlined in the foundational CNS 2.0 papers, our methodology for developing a next-generation Logic Critic is comprehensive and multi-faceted.

Stage 1: Rich Dataset Creation

A high-quality dataset is the bedrock of this project. Based on the strategy outlined in the IdeasPaper (Sec 5.2), we will go beyond simple “valid” vs. “invalid” labels.

  • Source Material: We will ingest a diverse corpus, including formal arguments from philosophical texts, case law from legal databases, and structured debates from scientific literature to create a seed set of real-world argument structures.
  • Synthetic Data Generation: We will develop a sophisticated generator for synthetic argument graphs. This will involve creating logically sound templates based on formal argumentation schemes and then applying a wide range of “fallacy transformations” to programmatically create challenging negative examples. This includes not just simple fallacies (e.g., ad hominem) but complex structural weaknesses like circular dependencies, evidential gaps, or unwarranted generalizations.
  • Fine-Grained Labeling: Graphs will be labeled with not just a binary score but with the type of fallacy present (e.g., circular_reasoning, unsupported_claim, internal_contradiction). This rich labeling is crucial for training a model that can provide explanatory feedback, moving the critic from a simple verifier to a diagnostic tool.
  • Human-in-the-Loop Validation: A panel of experts in formal logic and argumentation theory will validate all generated and annotated data to ensure its quality and consistency, establishing a gold-standard benchmark.

Stage 2: Advanced GNN Model Development

Our goal is to build a GNN architecture specifically designed for the nuances of logical reasoning. As proposed in the IdeasPaper (Sec 8.3), this involves moving beyond standard GNNs to a more specialized architecture.

  • Core Architecture: We will start by benchmarking standard architectures (GCN, GAT) but will move towards a custom model designed to process the unique structure of SNO Reasoning Graphs.
  • Key Innovations to be Explored:
    1. Hierarchical Attention: We will implement attention mechanisms that operate over reasoning sub-graphs, allowing the model to understand the structure of complex, multi-part arguments and weigh the importance of different lines of reasoning.
    2. Temporal Convolution: For SNOs where evidence evolves over time, we will explore incorporating temporal graph network components to model how the validity of a logical link can change with new information.
    3. Causal Integration: We will experiment with causal masking or other techniques to ensure the GNN learns to respect established causal relationships within the reasoning graph, preventing it from learning spurious correlations.
  • Training Objective: The model will be trained on a multi-task objective: to predict the overall LogicScore, to classify the type of fallacy (if any), and to identify the specific nodes or edges that are the source of the logical weakness.

Stage 3: Rigorous Evaluation and Explainable Integration

  • Evaluation: The GNN critic will be evaluated on a held-out test set, measuring its performance on both binary classification (sound/unsound) and the fine-grained fallacy detection task. We will compare its performance against both the baseline heuristic critic and human expert evaluations.
  • Error Analysis: We will conduct a detailed error analysis to understand not just when the model is wrong, but why. This will inform the next iteration of model development.
  • Explainability: A key requirement is that the GNN must be explainable. We will implement techniques like GNNExplainer to generate human-readable justifications for the model’s decisions by highlighting the sub-graph or specific reasoning chain that led to its judgment. This is critical for user trust and for the system’s overall transparency.
  • Integration: The final, validated GNN model will replace the heuristic-based LogicCritic in the main CNS 2.0 CriticPipeline, providing a more powerful and adaptive mechanism for ensuring logical coherence.

Expected Contribution

A successful GNN-based logic critic would be a state-of-the-art tool for automated reasoning. It would represent a significant advance over existing rule-based and heuristic methods by creating a system that learns the deep structural patterns of logical validity from data. This research would be a major step towards creating an AI system that can genuinely understand, evaluate, and provide feedback on the logical structure of complex arguments, forming a cornerstone of trustworthy AI.