28 September 2026 Dr. Vaishak Belle Professor Daxin Liu Professor Devendra Singh Dhami Professor Ondrej Kuzelka Dr. Efthymia Tsamoura Guest Editors, Special Issue on Neurosymbolic AI: First-Order Logic and Beyond Neurosymbolic Artificial Intelligence, IOS Press Dear Guest Editors, We are pleased to submit our revised manuscript entitled "A Trust-Centric Neuro-Symbolic Architecture for Verifiable Large Language Model Claims" (tracking number 980-2010) for consideration in the Special Issue on Neurosymbolic AI: First-Order Logic and Beyond in Neurosymbolic Artificial Intelligence. We thank the guest editors and the three reviewers for their thorough, constructive, and demanding feedback on the original submission. This paper addresses the growing concern over Large Language Model (LLM) hallucinations in safety-critical domains by formalising an architecture that integrates three previously separate capabilities: neural-to-symbolic grounding, provenance-weighted verification using Semantic Web trust mechanisms, and evidence-linked explanatory feedback. The key architectural contribution is the integration of digital signatures, source reputation, and provenance metadata into the verification decision, so that evidence is weighted by its provenance rather than treated uniformly. We also specify how these weights would enter a differentiable satisfiability objective. We believe the work fits naturally within the scope of this special issue. The core of our architecture is an NL to FOL translation layer (Stage A) that grounds LLM outputs into first-order logic before verification, directly addressing the special issue's focus on first-order logic in neurosymbolic systems. Our cascaded evaluation identifies this grounding step as the main bottleneck of the pipeline, which we report openly. Stage B specifies a provenance-weighted satisfiability objective and evaluates a rule-based verifier with conflict detection over a signed knowledge graph. Stage C closes the loop with structured, evidence-linked explanations that support human oversight and auditability, topics the call identifies under explainability, safety, and human-in-the-loop systems. In response to the reviewers' recommendations, this revision substantively rescales and substantiates the paper: 1. We have repositioned the contribution as an architectural framework and preliminary proof of concept, explicitly separating what is evaluated (a rule-based verifier over exact lookups) from what is specified (the differentiable LTN objective and grammar-masked decoding). 2. We established KG-relative reference verdicts for all 50 medical claims and report accuracy (0.72), macro-F1 (0.479) and an error analysis by logical complexity. Because the reference set is imbalanced (49 Verified, 1 Indeterminate, 0 Falsified), we also report that a constant Verified answer scores 0.98, and state that the evaluation measures support recovery rather than rejection of false claims. 3. We ran the Unweighted Verifier ablation (w_t = 1), which isolates the contribution of trust weighting: accuracy 0.66 against 0.72, a difference that is not statistically significant at this scale (McNemar p = 0.375). 4. We ran the cascaded evaluation, passing Stage A's predicted FOL into Stage B (accuracy 0.16), which identifies grounding as the main bottleneck. 5. We performed a sensitivity analysis over thresholds, trust coefficients and source reputations. A comprehensive point-by-point response addressing every reviewer comment in detail is enclosed in our separate response letter. In line with the journal's open data and software policy, the reference implementation, the curated medical-claims dataset with reference verdicts, the signed knowledge graph with verification keys, the evaluation scripts, and replication instructions will be made publicly available upon acceptance. The source code and data are available to reviewers upon request. Neither the manuscript nor any substantial part of it has been published or is under consideration elsewhere. We have read and agreed to the IOS Press Author Copyright Agreement and the journal's open and transparent review policy. We thank you and the reviewers for your time and guidance in strengthening this work. Sincerely, David Farrugia (corresponding author) Alexiei Dingli Department of Artificial Intelligence Faculty of ICT University of Malta Email: david.farrugia.15@um.edu.mt