Reviewer has chosen to be Anonymous

Overall Impression: Excellent

Content:
Technical Quality of the paper: Excellent
Originality of the paper: Yes
Adequacy of the bibliography: Yes

Presentation:
Adequacy of the abstract: Yes
Introduction: background and motivation: Good
Organization of the paper: Satisfactory
Level of English: Satisfactory
Overall presentation: Good

Detailed Comments:

This extended version significantly develops the original conference paper into a full journal contribution. The main contributions and novelty were already clear in the earlier version, and the issues previously noted by me have now been well addressed. The paper reads much more clearly, and the technical depth and experimental validation justify its extension to a journal publication.

Minor comments:

The Preliminaries section could be clearer. In particular, variable Y is introduced before being defined. Sections 2.1 and 2.2 would benefit from a short running example to illustrate the main concepts.

“The paper by Wagner and d’Avila Garcez (2021) has recently inaugurated” --> this phrasing should be updated, as the work is no longer recent.

“We integrate counterfactual fairness by estimating counterfactuals examples via current methods” --> perhaps clarify “current methods for counterfactuals.”

“can further devide” --> should be “can further divide.”

“this query could logically formulates as:” --> should be “this query could be logically formulated as.”

The second post-hoc query regarding counterfactual fairness for specific subgroups is mentioned but not shown or formally expressed. Is there a specific reason for omitting it?

Finally, I recommend that the manuscript be reviewed by a native English speaker to further improve style and flow.

Reviewer has chosen to be Anonymous

Overall Impression: Good

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes
Adequacy of the bibliography: Yes

Presentation:
Adequacy of the abstract: Yes
Introduction: background and motivation: Good
Organization of the paper: Satisfactory
Level of English: Satisfactory
Overall presentation: Excellent

Detailed Comments:

The authors propose a NeSy framework for counterfactual fairness using Logic Tensor Networks (LTN). Counterfactual fairness, subgroup fairness, and counterfactual knowledge-extraction requirements are encoded as first-order axioms on top of a neural classifier, and the model is trained by maximizing the overall LTN satisfaction. Experiments on standard fairness benchmarks show improved CF-MSE and worst-subgroup CF-MSE for competitive accuracy.

Strengths
- Intuitive axiomatization: The mapping from probabilistic counterfactual fairness to FO axioms is clear and easy to follow.

- Clear presentation: 
The paper is well written, with good preliminaries on causal models and LTNs. The experimental section is clearly organized into different research questions.

- Empirical evidence on multiple datasets: 
Experiments on Adult, COMPAS, COMPAS, and Lawschool show that LTN axioms systematically improves CF metrics with some accuracy trade-offs.

- Ease of use: I think the modularity of the approach, i.e., ease of incorporation into any training pipeline is a big strength.

- Post-hoc analysis via first-order logic queries: Beyond using axioms only during training, the authors cleverly leverage LTN framework to query the trained model and extract counterfactual knowledge.

Weakness:

- While the method enforces counterfactual fairness axioms in LTN, the paper does not provide a formal argument relating high fuzzy satisfaction of these axioms to the probabilistic condition in Eq. (1). I would encourage the authors to add at least a simple analysis for the specific LTN semantics used in the experiments (product t-norm conjunction, Reichenbach implication, p-mean quantifiers). For example, it would be helpful to clarify under which conditions (if any) a truth value of 1 for A4 on sampled factual–counterfactual pairs implies an empirical version of Eq. (1), and how partial truth values of A4 should be interpreted in terms of approximate counterfactual fairness.