Reviewer has chosen to be Anonymous

Overall Impression: Average

Content:
Technical Quality of the paper: Good
Originality of the paper: Yes, but limited
Adequacy of the bibliography: No

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

Detailed Comments:

This paper proposes the idea of a belief net, essentially a kind of belief structure based on graphical models within a neural symbolic pipeline. The concept is that this belief net enables the system to perform neural symbolic inference and learning in complex environments. Specifically, the authors are considering joint image and concept understanding problems in potentially multimodal situations where critical decisions must be made. This could involve scenarios such as autonomous vehicles operating in real-world environments.

They argue for a belief net in which the agent constructs and updates its model. The authors provide motivation and background on the setting, discussing a few neuro-symbolic approaches, including logic tensor networks and other related models. They explain how the agent updates its environment based on the graphical structure, possibly adding new concept nodes, detailing the actions that inform the agent's decision-making.

Overall, I find this to be an interesting and fairly complex problem, defined across several challenging environments. I also appreciate the application of logic tensor networks, which have typically been static models, to this dynamic setting. Arguably, beliefs and actions are essential for this to succeed. The authors seem to have a strong grasp of the problem, and Algorithm 1, for instance, goes into how new relations are formed.

However, I felt that the paper remains unpolished. While some equations are included, the discussion of the belief model feels ad hoc with minimal formal structure. It seems to be more of an empirical piece of work, where the authors have applied logic tensor networks to a setting that appears to necessitate a graphical model. This is not to say the work is trivial; rather, it lacks a rigorous and principled approach to the semantics and framework.

Moreover, there exists a substantial amount of related work discussing how belief states could be integrated with probabilistic programming and probabilistic relational modeling. For instance, consider research on relational affordances, problog applied to dynamic contexts, and distributional clauses in robot tracking and MDPs, MLNs to event modelling etc. Given that these pieces of work receive only a brief mention in the paper, it is hard to ascertain what is new and what constitutes a principled contribution in the broader context.

I acknowledge that the use of logic tensor networks represents a novelty and introduces several challenges, making this work relevant to the journal. However, I encourage the authors to study some of these related works closely and to develop a more disciplined presentation of the material, results, framework, and formal machinery to an acceptable standard. While this could suffice as a systems description paper, I believe that if it is to be part of the journal as a research contribution, it must meet higher standards regarding its formal development.

Reviewer has chosen to be Anonymous

Overall Impression: Average

Content:
Technical Quality of the paper: Average
Originality of the paper: Yes, but limited
Adequacy of the bibliography: No

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 article proposes a neuro-symbolic architecture for autonomous traversal of difficult terrain. The architecture combines beliefs and backpropagation. Its performance is evaluated in experiments on an offroad navigation dataset.

Strengths:
- Overall accessible to the reader. An informative contextual and historical overview in the introduction. A nice visualization of the traversibility risk challenge in Fig 1.
- An interesting explainable architecture intersecting Bayesian and neural reasoning. It appears novel, at least in the context of terrain traversability.
- The proposed approach mostly outperforms the baselines in extensive experiments.

The major weaknesses revolve around two aspects: some conceptual confusions and lack of consideration of relevant existing work. The details are listed below.

Some conceptual concerns:
- What is "caution" in the context of Figure 3?
- Brief examples would greatly help understand the otherwise abstract sections 5.1.2 and 5.1.3.
- Alg 1 is more of an example (which is appreciated), but the model building/updating also needs to be formalized in a general manner.
- In the training phase, it is not clear where the labels for traversibility come from. Their availability seems to contradict the

Missed related work:
- Does not consider two recent approaches to traversability:
- Neurosymbolic: "PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Driving"
- Self-supervised: "V-STRONG: Visual Self-Supervised Traversability Learning for Off-road Navigation"
- The discussion of beliefs is not grounded in the standard Bayesian causal models of Pearl: "Causality: Models, Reasoning and Inference"
- Does not consider the area of causal representation learning (and such techniques like Causal VAE): "Toward Causal Representation Learning"
- Does not consider how multimodality interacts with interpretability and performance in neurosymbolic architectures: "Surveying neuro-symbolic approaches for reliable artificial intelligence of things"

Minor issues:
- "symbolic information ensures that the evolution remains deterministic" - confusing?
- p3l17 "a world models"
- p3l21 "vision based systems" -> "vision-based systems"
- "2.2. neurosymbolic AI" -> "2.2. Neurosymbolic AI"
- It is not clear that it is worth dedicating an entire section 3 to what is essentially a paragraph
- p7l31: "The architecture at 2 shows" -> "The architecture in Figure 2 shows"
- Fig 2 text is not readable. Fig 3 font size can also be increased without making the figure larger.
- p11l21 "a-priori" -> "a priori"
- (multiple places) "adaption" -> "adaptation"

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: Good

Detailed Comments:

Strengths of the paper
1.Innovative neurosymbolic integration
The hybrid approach addresses fundamental AI challenges in autonomous navigation by combining reasoning with learning. Unlike conventional deep learning models that function as black boxes, BeliefNet offers a structured, interpretable decision-making process.
2. Contextual and adaptive learning
BeliefNet moves beyond static object classification by incorporating contextual cues, leading to more robust traversability predictions. This capability is particularly useful in unpredictable environments where terrain conditions evolve dynamically.
3. Zero-shot learning and generalization
BeliefNET demonstrates zero-shot learning. By leveraging belief nodes, BeliefNet can infer traversability for objects not present in the training set, reducing the data dependency that traditional models suffer from.
4. Explainability and human-machine interaction
Trust in autonomous systems is crucial, particularly in defense, search-and-rescue, and high-risk domains. BeliefNet enables transparency through its structured symbolic reasoning, allowing operators to understand and, if necessary, modify the system’s behavior.

Limitations and areas for improvement
1. Computational overhead
The added complexity of maintaining symbolic representations alongside neural components may introduce computational inefficiencies, especially in real-time applications. Future work should explore optimization techniques to improve inference speed. If the authors have done/any other mechanism where this is handled, please add in the revised version.
2. Evaluation metrics and benchmarks
The paper benchmarks BeliefNet against a Random Forest classifier and a graph embedding model. While these comparisons highlight strengths, further evaluations against state-of-the-art deep learning models (e.g., Transformers, Reinforcement Learning) would provide a more comprehensive performance assessment. Please add this in the revised version.
3. Practical deployment considerations
Although the paper presents theoretical and experimental validation, real-world deployment scenarios remain unexplored. Testing BeliefNet in diverse and extreme environments with autonomous vehicles would solidify its applicability.