Reviewer has chosen to be Anonymous

Overall Impression: Good

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes, but limited
Adequacy of the bibliography: Yes, but see detailed comments

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

Detailed Comments:

The paper aims to contribute towards the "realm of neurosymbolic reasoning." In particular the authors highlight the importance
of creating benchmarks for the field and discuss how metrics,
dataset selection, and formulation of reasoning tasks.
Several papers in the past have dealt with the issue
of developing benchmarks for neuro-symbolic learning and
reasoning, event considering what is today referred to
as multimodalities. Pioneering work dealing with
different reasoning approaches aboud. However, the
authors have not mentioned them or have not have access to
them. See in e.g. [1,2] for historic and recent references.
As regards graph representation and the connections between
graph neural networks and neuro-symbolic systems, recent
work have explored this relationship at lenght beyond
the domain of the papers mentioned by the authors, see e.g. [3,4,5,6].
The authors are more focused on ontological reasoning,
but neuro-symbolic reasoning goes well beyond that.
Regarding graph neural networks for reasoning
and learning, the prototypical GNN approach and framework
developed by [3] and the more recent [4,5,6]
have established stronger connections and relationships between
graph reasoning, learning, and the use and need of
benchmarks for neuro-symbolic AI. See the examples and experiments
mentioned in these papers [4-6].
Reference [2] also mentions the different approaches to
develop experiments to validate and enrich neuro-symbolic AI.
As regards the desiderata for benchmarking neuro-symbolic reasoning,
the works [7,8,9] tackle the important relationship between
argumentative and deductive reasoning in neuro-symbolic AI.
The recent volume in which [9] was published is also a relevant
source for benchmarks for not only symbolic AI reasoning,
but also to consider adapting and evolving the benchmarks used
in symbolic AI to the neuro-symbolic domain.

Although the work is indeed promising, some relevant related work that have tackled the issues worked on in this paper are missing.
For instance, the authors could have mentioned that there is long
history of contributions to knowledge knowledge representation and reasoning in neuro-symbolic AI. Again, this is mentioned only
in "en passant", although e.g. [1,2] cover these issued in more specific terms than the general statements made by the authors such as
"[...]neuro-symbolic reasoning involves integrating symbolic reasoning, which relies on
structured logic and formal knowledge representation, with neural network-based methods known for their capacity
to process large-scale, unstructured data and learn complex patterns from it" and "Neuro-symbolic reasoning is a sophisticated AI method aiming to make sense of complex application domains." Both [1,2] below
explain the issues above in detail. This would make justice to a long
history of the field in these aspects.

Perhaps one of the most interesting aspects of the paper is, as
I mentioned above, the desiderata for benchmarking.
Here I suggest the following.
1) Diverse benchmark scenarios. Have you considered diversity in
a wider scope? For instance, language diversity obviously impacts
the benchmarking development and the resulting experiments.
2) Controlled inconsistencies. Again, there is a long
history of paraconsistent reasoning in computational logic.
Also, reference to the field of
belief revision, that once was popular in AI,
knowledge representation and reasoning, can add to the discussion here.
Unfortunately, such literature is not that well-known in
the current ML community. See e.g. [10]. It is not hard to see papers
coming soon exploring belief revision, and inconssistencies in
the current popular LLM approaches.
3) Embeddings. Already in the early 2000s, a form of embeddings was
explored under translation algorithms that represented the
reasoning rules in neurosymbolic systems. See [1,2,11] and references
therein. The ammalgamation of logical rules and neural networks is
comprehensively explored in [11].
4) Assessment of the deductive capabilities of existing approaches:
Recent works have explored the limits of the deductive capabilities
of neuro-symbolic approaches based on GNNs. See e.g. [5,6,12,13].
Also, [14] shows how gnn like approaches for neurso-symbolic AI
can be used to solve combinatorial problems. The benchmars for
these particular applications can be relevant in the context
of this paper, if the authors see fit.
5. Success metrics and key performance indicators.
Here, the authors should consider whether or not the systems
will be sound. The discussion of this topic, again, has happened
over the last two decades in the neuro-symbolic AI community.
Most papers that developed approaches to argumentation, temporal, modal
or epistemic reasoning and the experiments described in these papers
have referred to the metaproperties of logical system within
the neuro-symbolic paradigm, see e.g [15].

Considering the above, I would recommend that the paper is accepted
if such minor suggestions made above are taken into account.

[1] Sebastian Bader, Pascal Hitzler:
Dimensions of Neural-symbolic Integration - A Structured Survey. We Will Show Them! (1) 2005: 167-194.
@inproceedings{DBLP:conf/birthday/BaderH05,
author = {Sebastian Bader and
Pascal Hitzler},
editor = {Sergei N. Art{\"{e}}mov and
Howard Barringer and
Artur S. d'Avila Garcez and
Lu{\'{\i}}s C. Lamb and
John Woods},
title = {Dimensions of Neural-symbolic Integration - {A} Structured Survey},
booktitle = {We Will Show Them! Essays in Honour of Dov Gabbay, Volume One},
pages = {167--194},
publisher = {College Publications},
year = {2005},
timestamp = {Thu, 09 Jul 2020 09:13:39 +0200},
biburl = {https://dblp.org/rec/conf/birthday/BaderH05.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

[2] Artur d'Avila Garcez, Luís C. Lamb:
Neurosymbolic AI: the 3rd wave. Artif. Intell. Rev. 56(11): 12387-12406 (2023)
@article{DBLP:journals/air/GarcezL23,
author = {Artur d'Avila Garcez and
Lu{\'{\i}}s C. Lamb},
title = {Neurosymbolic {AI:} the 3rd wave},
journal = {Artif. Intell. Rev.},
volume = {56},
number = {11},
pages = {12387--12406},
year = {2023},
url = {https://doi.org/10.1007/s10462-023-10448-w},
doi = {10.1007/S10462-023-10448-W},
timestamp = {Sat, 14 Oct 2023 20:13:42 +0200},
biburl = {https://dblp.org/rec/journals/air/GarcezL23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

[3] Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., & Monfardini, G. (2008). The graph neural network model. IEEE transactions on neural networks, 20(1), 61-80.
@article{scarselli2008graph,
title={The graph neural network model},
author={Scarselli, Franco and Gori, Marco and Tsoi, Ah Chung and Hagenbuchner, Markus and Monfardini, Gabriele},
journal={IEEE transactions on neural networks},
volume={20},
number={1},
pages={61--80},
year={2008},
publisher={IEEE}
}
[4] Henrique Lemos, Pedro H. C. Avelar, Marcelo O. R. Prates, Artur S. d'Avila Garcez, Luís C. Lamb:
Neural-Symbolic Relational Reasoning on Graph Models: Effective Link Inference and Computation from Knowledge Bases. ICANN (1) 2020: 647-659
@inproceedings{DBLP:conf/icann/0001APGL20,
author = {Henrique Lemos and
Pedro H. C. Avelar and
Marcelo O. R. Prates and
Artur S. d'Avila Garcez and
Lu{\'{\i}}s C. Lamb},
editor = {Igor Farkas and
Paolo Masulli and
Stefan Wermter},
title = {Neural-Symbolic Relational Reasoning on Graph Models: Effective Link
Inference and Computation from Knowledge Bases},
booktitle = {Artificial Neural Networks and Machine Learning - {ICANN} 2020 - 29th
International Conference on Artificial Neural Networks, Bratislava,
Slovakia, September 15-18, 2020, Proceedings, Part {I}},
series = {Lecture Notes in Computer Science},
volume = {12396},
pages = {647--659},
publisher = {Springer},
year = {2020},
url = {https://doi.org/10.1007/978-3-030-61609-0\_51},
doi = {10.1007/978-3-030-61609-0\_51},
timestamp = {Thu, 10 Nov 2022 17:26:23 +0100},
biburl = {https://dblp.org/rec/conf/icann/0001APGL20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

[5] Abboud, R., Ceylan, I. I., Grohe, M., & Lukasiewicz, T. (2020). The surprising power of graph neural networks with random node initialization. arXiv preprint arXiv:2010.01179.
@article{abboud2020surprising,
title={The surprising power of graph neural networks with random node initialization},
author={Abboud, Ralph and Ceylan, Ismail Ilkan and Grohe, Martin and Lukasiewicz, Thomas},
journal={arXiv preprint arXiv:2010.01179},
year={2020}
}

[6]Luis C. Lamb, Artur S. d'Avila Garcez, Marco Gori, Marcelo O. R. Prates, Pedro H. C. Avelar, Moshe Y. Vardi:
Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective. IJCAI 2020: 4877-4884
@inproceedings{DBLP:conf/ijcai/LambGGPAV20,
author = {Lu{\'{\i}}s C. Lamb and
Artur S. d'Avila Garcez and
Marco Gori and
Marcelo O. R. Prates and
Pedro H. C. Avelar and
Moshe Y. Vardi},
editor = {Christian Bessiere},
title = {Graph Neural Networks Meet Neural-Symbolic Computing: {A} Survey and
Perspective},
booktitle = {Proceedings of the Twenty-Ninth International Joint Conference on
Artificial Intelligence, {IJCAI} 2020},
pages = {4877--4884},
publisher = {ijcai.org},
year = {2020},
url = {https://doi.org/10.24963/ijcai.2020/679},
doi = {10.24963/IJCAI.2020/679},
timestamp = {Mon, 20 Jul 2020 12:38:52 +0200},
biburl = {https://dblp.org/rec/conf/ijcai/LambGGPAV20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

[7] Maurizio Proietti, Francesca Toni:
A Roadmap for Neuro-argumentative Learning. NeSy 2023: 1-8
@inproceedings{DBLP:conf/nesy/ProiettiT23,
author = {Maurizio Proietti and
Francesca Toni},
editor = {Artur S. d'Avila Garcez and
Tarek R. Besold and
Marco Gori and
Ernesto Jim{\'{e}}nez{-}Ruiz},
title = {A Roadmap for Neuro-argumentative Learning},
booktitle = {Proceedings of the 17th International Workshop on Neural-Symbolic
Learning and Reasoning, La Certosa di Pontignano, Siena, Italy, July
3-5, 2023},
series = {{CEUR} Workshop Proceedings},
volume = {3432},
pages = {1--8},
publisher = {CEUR-WS.org},
year = {2023},
url = {https://ceur-ws.org/Vol-3432/paper1.pdf},
timestamp = {Tue, 11 Jul 2023 17:14:10 +0200},
biburl = {https://dblp.org/rec/conf/nesy/ProiettiT23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

[8] Artur S. d'Avila Garcez, Dov M. Gabbay, Luís C. Lamb:
A neural cognitive model of argumentation with application to legal inference and decision making. J. Appl. Log. 12(2): 109-127 (2014)
@article{DBLP:journals/japll/GarcezGL14,
author = {Artur S. d'Avila Garcez and
Dov M. Gabbay and
Lu{\'{\i}}s C. Lamb},
title = {A neural cognitive model of argumentation with application to legal
inference and decision making},
journal = {J. Appl. Log.},
volume = {12},
number = {2},
pages = {109--127},
year = {2014},
url = {https://doi.org/10.1016/j.jal.2013.08.004},
doi = {10.1016/J.JAL.2013.08.004},
timestamp = {Tue, 16 Feb 2021 08:56:04 +0100},
biburl = {https://dblp.org/rec/journals/japll/GarcezGL14.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

[9] Gopal Gupta, Huaduo Wang, Kinjal Basu, Farhad Shakerin, Elmer Salazar, Sarat Chandra Varanasi, Parth Padalkar, Sopam Dasgupta:
Logic-Based Explainable and Incremental Machine Learning. 346-358
In: David Scott Warren, Verónica Dahl, Thomas Eiter, Manuel V. Hermenegildo, Robert A. Kowalski, Francesca Rossi:
Prolog: The Next 50 Years. Lecture Notes in Computer Science 13900, Springer 2023, ISBN 978-3-031-35253-9

@incollection{DBLP:series/lncs/0001W0SSVPD23,
author = {Gopal Gupta and
Huaduo Wang and
Kinjal Basu and
Farhad Shakerin and
Elmer Salazar and
Sarat Chandra Varanasi and
Parth Padalkar and
Sopam Dasgupta},
editor = {David Scott Warren and
Ver{\'{o}}nica Dahl and
Thomas Eiter and
Manuel V. Hermenegildo and
Robert A. Kowalski and
Francesca Rossi},
title = {Logic-Based Explainable and Incremental Machine Learning},
booktitle = {Prolog: The Next 50 Years},
series = {Lecture Notes in Computer Science},
volume = {13900},
pages = {346--358},
publisher = {Springer},
year = {2023},
url = {https://doi.org/10.1007/978-3-031-35254-6\_28},
doi = {10.1007/978-3-031-35254-6\_28},
timestamp = {Mon, 14 Aug 2023 21:18:03 +0200},
biburl = {https://dblp.org/rec/series/lncs/0001W0SSVPD23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
[10] Darwiche, Adnan, and Judea Pearl. "On the logic of iterated belief revision." Artificial intelligence 89.1-2 (1997): 1-29.
@article{darwiche1997logic,
title={On the logic of iterated belief revision},
author={Darwiche, Adnan and Pearl, Judea},
journal={Artificial intelligence},
volume={89},
number={1-2},
pages={1--29},
year={1997},
publisher={Elsevier}
}
[11] Garcez, Artur S.D'Avila, Luis C. Lamb, and Dov M. Gabbay. Neural-symbolic cognitive reasoning. Springer Science & Business Media, 2009.
@book{DBLP:series/cogtech/GarcezLG2009,
author = {Artur S. d'Avila Garcez and
Lu{\'{\i}}s C. Lamb and
Dov M. Gabbay},
title = {Neural-Symbolic Cognitive Reasoning},
series = {Cognitive Technologies},
publisher = {Springer},
year = {2009},
url = {https://doi.org/10.1007/978-3-540-73246-4},
doi = {10.1007/978-3-540-73246-4},
isbn = {978-3-540-73245-7},
timestamp = {Tue, 16 May 2017 14:24:26 +0200},
biburl = {https://dblp.org/rec/series/cogtech/GarcezLG2009.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
[12] Martin Grohe: The Descriptive Complexity of Graph Neural Networks. LICS 2023: 1-14
@inproceedings{DBLP:conf/lics/Grohe23,
author = {Martin Grohe},
title = {The Descriptive Complexity of Graph Neural Networks},
booktitle = {{LICS}},
pages = {1--14},
year = {2023},
url = {https://doi.org/10.1109/LICS56636.2023.10175735},
doi = {10.1109/LICS56636.2023.10175735},
timestamp = {Thu, 20 Jul 2023 11:32:59 +0200},
biburl = {https://dblp.org/rec/conf/lics/Grohe23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
[13] Martin Grohe: The Logic of Graph Neural Networks. LICS 2021: 1-17
@inproceedings{DBLP:conf/lics/Grohe21,
author = {Martin Grohe},
title = {The Logic of Graph Neural Networks},
booktitle = {36th Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS}
2021, Rome, Italy, June 29 - July 2, 2021},
pages = {1--17},
publisher = {{IEEE}},
year = {2021},
url = {https://doi.org/10.1109/LICS52264.2021.9470677},
doi = {10.1109/LICS52264.2021.9470677},
timestamp = {Fri, 09 Jul 2021 14:36:19 +0200},
biburl = {https://dblp.org/rec/conf/lics/Grohe21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
[14] Jan Tönshoff, Martin Ritzert, Hinrikus Wolf, Martin Grohe:
Graph Neural Networks for Maximum Constraint Satisfaction. Frontiers Artif. Intell. 3: 580607 (2020)
@article{DBLP:journals/frai/TonshoffRWG20,
author = {Jan T{\"{o}}nshoff and
Martin Ritzert and
Hinrikus Wolf and
Martin Grohe},
title = {Graph Neural Networks for Maximum Constraint Satisfaction},
journal = {Frontiers Artif. Intell.},
volume = {3},
pages = {580607},
year = {2020},
url = {https://doi.org/10.3389/frai.2020.580607},
doi = {10.3389/FRAI.2020.580607},
timestamp = {Tue, 02 Mar 2021 23:07:15 +0100},
biburl = {https://dblp.org/rec/journals/frai/TonshoffRWG20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
[15] Artur S. d'Avila Garcez, Luís C. Lamb, Dov M. Gabbay:
Connectionist computations of intuitionistic reasoning. Theor. Comput. Sci. 358(1): 34-55 (2006)

Reviewer has chosen to be Anonymous

Overall Impression: Good

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes, but limited
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 is a position paper that makes the case that careful thought about evaluation is necessary to make real progress in neuro-symbolic reasoning. The main contributions of the paper are: 1. Table 1, which illustrates the diversity of neuro-symbolic reasoning approaches and evaluations, and 2. Desiderata for benchmarking neuro-symbolic reasoners.

The paper highlights several critical issues and makes a good case for a comprehensive benchmarking framework to support this type of research. Of course, as a position paper, it does not propose a solution, but the paper will serve to guide future researchers. I think the list of desiderata will be particularly helpful in this regard.

One issue that is not addressed directly, but could be mentioned, is that the framework should support (to the extent possible) purely neural approaches, e.g., large language models. Neural approaches may not perform well on all tasks, but it should be possible to include them as a baseline.

Detailed comments
Page 1, line 20: Not all neuro-symbolic approaches use symbolic logic, e.g., neuro-symbolic planners.
Page 2, lines 2-16: The five categories given do not match up with those given in reference 9. Kautz has 6 categories and uses a different notation in places. The authors need to explain how/why they deviated from Kautz.
Page 2, line 20-21: Should read “The primary purposes of such a benchmark are two-fold.”
Page 2, line 37: Should read “other reasoning tasks” (no “the”) since this is not a comprehensive list.
Page 5, lines 37-43: This information should be included in Table 1 if possible rather than in the text after the table.
Page 6, lines 13-20: Regarding controlled inconsistencies: It might be helpful to have an example here, as some readers may not understand the importance of this issue.
Page 7, line 12: This seems to be an additional desideratum (i.e., a “living” benchmark) that could be included in the list on page 6. Many of the larger benchmarks for LLMs seem to be allowing for adaptation over time. Of course this brings in additional issues (benchmark versioning and comparing over time) but the short shelf life of many benchmark tasks makes this necessary.

Reviewer has chosen to be Anonymous

Overall Impression: Good

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes, but limited
Adequacy of the bibliography: Yes, but see detailed comments

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

Detailed Comments:

This paper posits that we need to benchmark NS reasoners. It then surveys NS reasoning
evaluation setups and points out to the variation of metrics and datasets that prevents
meaningful conclusions. They then list other desiderata like representation and metrics
that are representative of NS variety and needs holistic consideration like terminologies
and scenarios.

The paper is on the right track but the current writeup is a bit premature and vague
for the venue to judge its long-term impact. The paper is missing examples to illustrate
authors' case. It could have put forth a desired benchmark, even to a narrow scope, that
would be a big contribution making their desiderata easy to check for completeness and
others to agree/ enhance.

Overall, a good idea but premature paper without a concrete benchmark proposed.