Technical Summary: Neurosymbolic Learning for Inference-Time Argumentation

Problem Statement

Claim verification is a critical task in high-stakes domains such as healthcare, finance, and scientific discovery. While Large Language Models (LLMs) have shown promise in this area, standard binary classification (True/False) is often insufficient when underlying information is incomplete or conflicting. In such cases, an "Uncertain" verdict is more appropriate than a forced binary decision. Furthermore, in high-stakes settings, the explanations for these verdicts must be faithful—meaning the reasoning process must genuinely reflect the factors determining the final decision, rather than relying on post-hoc rationalizations that may be unfaithful to the model's internal logic.

Existing approaches often treat argumentation as an inference-time explanation layer or rely on off-the-shelf LLMs to generate arguments without optimizing them for the specific verification task. Additionally, many reinforcement learning (RL) approaches for reasoning focus on tasks with verifiable, deterministic outcomes (e.g., mathematics), failing to address the inherent uncertainty of claim verification where outcomes may be ambiguous.

Methodology: Inference-Time Argumentation (ITA)

The authors introduce Inference-Time Argumentation (ITA), a trainable neurosymbolic framework designed for ternary claim verification (True, False, Uncertain). Unlike previous methods that use argumentation solely for explanation, ITA integrates formal argumentation semantics directly into the training loop to guide both argument generation and scoring.

Core Framework

The system operates on Quantitative Bipolar Argumentation Frameworks (QBAFs):

1. Argument Generation: An LLM (parameterized by $\theta$) generates a set of supporting ($S_c$) and attacking ($T_c$) arguments for a given claim $c$. The claim itself is treated as an argument $a_c$.
2. Base Score Assignment: A learnable Base Score Model (BSM) (parameterized by $\phi$) assigns an intrinsic strength (base score) $\tau(a) \in [0, 1]$ to each generated argument. The claim's base score is fixed at a neutral prior of 0.5.
3. Semantic Aggregation: A deterministic argumentation semantics function, DF-QuAD, aggregates the base scores and the support/attack relations to compute a final argumentative strength $\hat{v}_c = \sigma(a_c)$ for the claim.
4. Verdict Derivation: The final strength is mapped to a ternary verdict using fixed thresholds:
   • False: $\hat{v}_c \leq 1/3$
   • True: $\hat{v}_c \geq 2/3$
   • Uncertain: $1/3 < \hat{v}_c < 2/3$

Training Strategies

ITA employs two distinct training phases to optimize the components:

1. Weakly Supervised Learning for Base Scores (BSM):

   • Priming Phase: The regression head of the BSM is initialized using supervised learning on triples of (claim, argument, base score), where scores are generated by prompting a base LLM.
   • Semantic Loss Phase: The BSM is fine-tuned using a neurosymbolic loss function. The loss is the Mean Squared Error (MSE) between the predicted claim strength (derived via DF-QuAD) and the ground-truth label (mapped to 0, 0.5, or 1). Since DF-QuAD is differentiable, gradients can be back-propagated through the semantics to update the BSM.
   • Auxiliary Losses: To improve local properties, the authors introduce Consistency Loss (minimizing variance for semantically equivalent arguments) and Ranking Loss (enforcing a predefined ordering of argument quality).

2. Reinforcement Learning for Argument Generation:

   • The argument generator is optimized using Group Relative Policy Optimization (GRPO).
   • Reward Function: The reward is derived from the final claim strength $\hat{v}_c$ produced by the BSM and DF-QuAD. It provides maximum reward for strengths that fall within the correct classification interval (e.g., high strength for "True" labels) and linearly decreasing rewards as the strength moves away from the correct threshold. This turns the argumentation semantics into a training signal, encouraging the generator to produce arguments that lead to correct verdicts.

Key Contributions

1. Trainable Neurosymbolic Framework: The introduction of ITA, which extends the role of argumentation from a static inference-time explanation layer to a dynamic learning interface where semantics guide model training.
2. Optimization Strategies: The proposal of two novel training strategies:
   • Learning base scores via downstream argumentative verdicts rather than relying solely on static LLM scores.
   • Using formal argumentation semantics to generate rewards for reinforcement learning, optimizing argument generation for the specific task of claim verification.
3. Faithful Explainability: By construction, the final verdict is a deterministic function of the generated arguments, their learned scores, and the semantics. This ensures the explanation is faithful to the decision process, avoiding the pitfalls of post-hoc reasoning traces.

Experimental Results

The authors evaluated ITA on two ternary claim verification datasets: TFU Evaluation Claims (derived from StrategyClaim and DEBATunE) and AVeriTeC (real-world claims). They compared ITA against non-argumentative baselines (direct prediction via SFT and GRPO) and argumentative baselines (using off-the-shelf LLMs for arguments and scores).

• Performance:

  • Base Score Models: Learned BSMs significantly outperformed argumentative baselines that used constant or prompted scores. The best-performing BSM (trained on GPT-5 generated arguments with semantic, ranking, and consistency losses) achieved 0.677 accuracy on TFU and 0.460 balanced accuracy on AVeriTeC, outperforming all faithfully explainable baselines and competing with the strongest direct-prediction baselines.
  • Argument Generators: Training the argument generator via GRPO yielded mixed but positive results, showing slight improvements over untrained generators when paired with prompted scores, though the gains were less consistent than those from training the BSM.
  • Combination: Combining a trained generator with a trained BSM did not yield additive improvements over the best BSM alone, suggesting that the scorer is calibrated to a specific argument distribution.

• Local Properties: Training with auxiliary losses significantly improved the consistency of scores for paraphrased arguments and the ranking of arguments by quality, demonstrating that the framework can learn desirable local properties beyond just downstream accuracy.

Significance and Claims

The paper claims that ITA demonstrates that formal argumentation semantics can serve as a useful training signal for LLMs, not just as an inference-time aggregation rule. By integrating argumentation into the training loop, the system achieves competitive performance with direct prediction methods while maintaining procedural faithfulness—the verdict is explicitly derived from inspectable argumentative structures.

The authors position this work as a step toward more transparent and reliable AI in high-stakes domains, where the ability to explain why a claim is uncertain or false is as important as the classification itself. They acknowledge limitations, including the lack of external evidence retrieval (arguments are generated from model knowledge) and the restriction to depth-1 argumentation frameworks, noting these as directions for future work.