ForEx: A Formal Verification Framework for Explainable Reasoning in Logical Fallacy Detection and Annotation

2026-06-20

AI Summary

This work addresses a critical limitation in current large language models (LLMs) for logical fallacy detection: their focus on predicting labels while neglecting whether the natural language explanations they generate are amenable to formal verification. To bridge this gap, the authors propose the ForEx framework, which automatically translates LLM-generated explanations into Lean4 formal language and evaluates whether the reasoning chain is formally derivable from encoded premises—rather than directly assessing the validity of the original argument. By introducing an LLM argument validation matrix, this study pioneers machine-verifiable analysis of explanatory reasoning, explicitly distinguishing between label consistency and formal derivability. Experiments on the LOGIC-Climate dataset reveal that over 90% of model-generated explanations pass formal verification, yet only about 20% align with human annotations, exposing a significant systematic discrepancy between formal correctness and human judgment.

Abstract

Current evaluations of Large Language Models (LLMs) on logical fallacy detection focus on predicted labels, but do not establish whether those labels are supported by the reasoning the models provide. We propose ForEx (Formal Verification for Explainable Reasoning), a framework that translates LLM-generated explanations into Lean4 and verifies whether the translated rationale is derivable under encoded premises, not the logical validity of the original natural language argument. To distinguish prediction outcomes from the formal status of the supporting reasoning, we introduce the LLM Argument Verification Matrix, which separates label consistency from formal verification status. Experiments on LOGIC-Climate show that over 90% of LLM outputs can be translated into formal reasoning chains that pass verification, while agreement with human annotations remains around 20%. These results expose a systematic gap between formal derivability and label agreement, a distinction invisible to prediction-based metrics. ForEx moves LLM evaluation beyond label correctness toward machine-checkable analysis of formalized reasoning chains.

Problem

• logical fallacy detection
• explainable reasoning
• formal verification
• large language models
• reasoning evaluation

Innovation

• formal verification
• explainable reasoning
• logical fallacy detection
• Lean4
• LLM evaluation