Expressivity Results for Structured Argumentation Frameworks with Uncertain Rules and Premises

This paper studies the expressive power of ASPIC$^+$ argumentation frameworks with uncertain preference profiles by comparing them with several abstract formalisms with uncertain defeats. Most of our results are negative (and some of them are theoretically unexpected). We also conjecture a positive, non-trivial threshold for the expressivity of uncertain preferences, and prove some essential preliminary steps toward the confirmation of this conjecture.

ASPIC-style structured argumentation frameworks provide a formal basis for reasoning in artificial intelligence by combining internal argument structure with abstract argumentation semantics. A key challenge in these frameworks is ensuring compliance with five critical rationality postulates: closure, direct consistency, indirect consistency, non-interference, and crash-resistance. Recent approaches, including ASPIC$^{\ominus}$ and Deductive ASPIC$-$, have made significant progress but fall short of meeting all postulates simultaneously under a credulous semantics (e.g. preferred) in the presence of undercuts. This paper introduces Deductive ASPIC$^{\ominus}$, a novel framework that integrates gen-rebuttals from ASPIC$^{\ominus}$ with the Joint Support Bipolar Argumentation Frameworks (JSBAFs) of Deductive ASPIC$-$, incorporating preferences. We show that Deductive ASPIC$^{\ominus}$ satisfies all five rationality postulates under a version of preferred semantics. This work opens new avenues for further research on robust and logically sound structured argumentation systems.

Reliable uncertainty estimation is essential for deploying large language models in high-stakes reasoning tasks, yet most existing approaches rely on expensive sampling strategies or shallow token-level signals that ignore the internal logical structure of model outputs. We introduce Argument Graph Uncertainty, a post-hoc framework for multiple choice question tasks, that estimates model confidence directly from the logical structure of a single chain-of-thought reasoning trace. Our method uses either a lightweight instruction-tuned model or a simple deterministic rule to segment the reasoning chain into propositional units, then applies a NLI model to infer relational edges and construct two complementary argument graphs over these segments. The resulting edge scores are aggregated into a Dirichlet posterior over answer options, whose concentration yields calibrated uncertainty estimates reflecting both local step-to-step coherence and global logical consistency across the reasoning trace. Evaluated on GPQA, MMLU-Pro and TruthfulQA, our method consistently surpasses token-based and consistency-based uncertainty baselines across multiple reasoning models. We further demonstrate through extensive combination analyses that argument graph uncertainty captures an orthogonal signal to existing approaches, making it a complementary component in uncertainty ensembles. Crucially, our framework requires no additional calls to the evaluated model and relies entirely on small, efficient auxiliary models, producing fully interpretable, per-node uncertainty attributions at low computational cost.