Position: Logical Soundness is not a Reliable Criterion for Neurosymbolic Fact-Checking with LLMs

Misinformation that cites legitimate papers can be especially harmful when it distorts what those studies actually report. While existing automatic fact-checking systems based on large language models (LLMs) can assess whether a model assigns an Incorrect verdict and can gen- erate explanations for that decision, they typi- cally do not indicate whether the model follows the same reasoning path as human experts or arrives at the verdict through a different but still valid path. In this work, we introduce a graph- based framework (typed reasoning graph) for comparing human and LLM reasoning paths in scientific fact-checking. Building on prior work on fallacious reasoning in biomedical misinformation, MISSCIPLUS (Glockner et al., 2025), we model each explanation as a rea- soning graph that links the false claim to the relevant study context, study findings, fallacy- supporting premises, and fallacy labels. This representation enables one-to-one alignment of human and LLM reasoning at the level of fallacy-specific sub-graphs. For non-human- aligned LLM paths, we validate grounding in the cited study, relevance to the claim, and suf- ficiency for the verdict. Using 84 false claims from MISSCIPLUS, we evaluate GPT-5, Claude Opus 4.7, and Qwen3-32B across prompt and evidence settings. Results show distinct perfor- mance dimensions: Qwen3-32B has the lowest verdict failure rate, GPT-5 the highest human alignment, and Claude Opus 4.7 weak verdict prediction but often valid reasoning in success- ful cases

Humans naturally form and express beliefs in daily communication, e.g., "I think the answer is 3" or "I suppose that's right." Such beliefs inevitably intertwine with fact and knowledge, making the ability to handle them in tandem desirable for large language models (LLMs), as they are increasingly deployed in user-facing settings. Prior work showed that even capable LLMs exhibit a systemic weakness in acknowledging user beliefs grounded in incorrect information. We extend this evaluation to 10 LLMs across 18 epistemic expressions and find that the size and direction of this weakness depend on the verb used to express the belief, with the accuracy gap between factual and false information ranging from +50% on "I vaguely remember" to -14% on "I seriously doubt". We further show that the phenomenon stems from what we call task confusion: models default to fact-checking the underlying claim, overriding the user's stated belief. We provide evidence where chains of thought that explicitly fact-check show lower accuracy on false information than those that do not, and a single instruction can reverse the failure across verb families. Mechanistically, models attend more to false beliefs they fail to confirm, but suppressing this attention at decoding time recovers accuracy only partially and only in some models, calling for future work on intervention methods. Our findings clarify prior results and show how fact-checking, a generally desirable behavior, can interfere with belief tracking in LLMs.

Large language models (LLMs) increasingly serve as data-driven reasoners, yet their chains-of-thought (CoT) can be unfaithful even when final answers are correct. Most existing verification'' signals are not diagnostic: answer matching observes only the outcome, LLM-as-judge provides subjective and non-verifiable critiques, and scalar rewards (e.g., PRMs/RMs) offer little insight into where a multi-step derivation fails.We propose **SymDiag**, a neuro-symbolic framework that **reframes reasoning verification as structured failure diagnosis**. SymDiag translates natural-language CoT into symbolic constraints and performs step-level satisfiability/entailment checks to (i) localize failing steps and (ii) produce verifiable diagnostic evidence, including counterexamples, inconsistency witnesses, and missing-premise indicators. A central challenge is that apparent logic violations'' can be caused either by genuine reasoning defects or by neural-to-symbolic translation noise. SymDiag therefore incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability. Across diverse mathematical, logical, scientific, and general reasoning benchmarks, SymDiag improves detection of unfaithful reasoning and provides substantially more effective feedback for multi-round reasoning repair than outcome-only verification and LLM-based judging, offering a principled foundation for trustworthy and scalable reasoning diagnosis.