Subject: Submission of Manuscript for Special Issue on NeSy 2025 Extended Papers – A Neurosymbolic Approach to Counterfactual Fairness -------- Dear editors, We kindly ask you to consider the present manuscript, ``A Neurosymbolic Approach to Counterfactual Fairness", for publication in the Special Issue on NeSy 2025 of NAI. We believe this work aligns well with the scope of the special issue and will be of significant interest to your readership. This manuscript presents a novel integration of counterfactual fairness into neurosymbolic machine learning, specifically utilizing Logic Tensor Networks (LTN). We address the gap in research applying neurosymbolic methods to counterfactual fairness by formulating both accuracy and fairness constraints in first-order logic, enabling simultaneous optimization for performance and fairness. Experiments on three benchmark datasets demonstrate that this neurosymbolic approach achieves superior levels of counterfactual fairness, alongside benefits of interpretability and flexibility in handling subgroup fairness, compared to three recent methodologies. We would like to clarify that the present paper extends prior work of ours which we published at NeSy2025. Specifically, this version incorporates the following key differences and improvements compared to the NeSy submission: * Expanded Background and Context: We have significantly broadened the introductory sections, providing a more comprehensive overview of the bias mitigation landscape. We also sought to make the paper more self-contained by introducing the theoretical background required in understanding our method in a dedicated section. Compared to our NeSy2025 paper, we believe that the present manuscript is much more accessible, esp. as towards the NAI audience. * Post-hoc query and counterfactual knowledge extraction: extended methodology: One of the selling points of the methodology we present in the manuscript is the capability to obtain insights on a trained model via first-order logic queries. Compared to our NeSy2025 paper, we provide a full theoretical account of how this mechanism may be employed. Furthermore, we provide a detailed motivation and in-depth explanation of the Counterfactual Knowledge Extraction axioms (Section 4.3), clarifying their role and contribution to the overall framework. * Extended Experimental Evaluation with Novel Research Question: We have augmented the experimental evaluation with a new research question (Q4), investigating potential applications of post-hoc queries. We explicitly confirm that all authors have reviewed and approved the submission. Thank you for your time and consideration. We look forward to hearing from you soon. Sincerely, Xenia Heilmann, Chiara Manganini, Mattia Cerrato, Leonhard Kestel and Vaishak Belle