A Fragility-Aware Argumentation Framework for Epistemic Risk Propagation: Formalization and a Case Study in Kalām Reasoning

Computational argumentation offers graph-based formalisms for evaluating the strength of contested claims, and a growing body of work embeds large language models (LLMs) inside such graphs to produce explainable, contestable assessments. However, existing quantitative argumentation frameworks aggregate an argument’s strength from a single, largely undifferentiated notion of “base score” or “confidence,” without distinguishing why a reasoning path is uncertain. We argue that at least three sources of uncertainty are conflated in this treatment: (i) dependence on an open, unresolved question in the relevant field; (ii) a gap between a claim and the evidence available to support it; and (iii) the presence of a live, unrebutted objection. We propose a Fragility-Aware Reasoning Architecture that decomposes claims into an argument graph, tags each edge with a typed uncertainty source, and propagates a scalar Argument Fragility Index (AFI) through the graph using a variant of gradual argumentation semantics. Unlike prior work on epistemic and quantitative bipolar argumentation, our formalism treats fragility as a property of a reasoning path rather than only of a terminal conclusion, and supports dynamic routing away from fragile sub-paths. We position the framework relative to gradual and epistemic argumentation, argumentative LLMs, claim-decomposition verification pipelines, and the separate literature on LLM robustness to input perturbation, and we outline a demonstration domain — classical Islamic theological argumentation (Kalam) — chosen because its arguments are long-standing, informally structured, and rich in live philosophical objections and metaphysical premises whose status is contested rather than empirically resolved. We close with the paper’s current limitations and the validation steps required before its central claims can be considered established.