Enhancing Human-AI Collaboration Through Logic-Guided Reasoning

Q1:More discussions comparing the proposed approach to related studies need to be provided.

A1:In our original submission, because of the page limitation in the main paper, the description of the related work is provided in the supplementary material Section 2. It includes a comprehensive overview of the literature (including behavior understanding, logical reasoning, and human-robot interaction) related to our work. We apologize for not including the related work directly in the main document and have added it into our revised manuscript.

Q2: Moreover, some parts of the method explanation are somewhat hard to follow.

A2: Thank you for your feedback. The query, denoted as v=(a, s), actually represents a tuple consisting of an action and a state. We have added specifications for these variables in a revision.

Q3:I list some minor comments.

A3: Thank you for your suggestion. In our formulation, although f represents a rule, it is also conceptualized as a set comprising all the predicates that constitute the rule. This dual characterization allows us to employ set notation to encapsulate the composite elements of the rule f. Moreover, we also add [1,2] in the related work and analyze their novelty clearly.

[1] Artur d'Avila Garcez, Luís C. Lamb: Neurosymbolic AI: the 3rd wave. Artif. Intell. Rev. 56(11): 12387-12406 (2023)

[2] Henry Kautz. The Third AI Summer: AAAI Robert S. Engelmore Memorial Lecture. AI Magazine, 43(1), 105-125 (2022).

Q4: What are the most related studies?

A4: In Section 3.2, we describe several related studies (including WAH, which is the most related study) and provide a brief summary of the novelty of these methods. Moreover, in our experiment, we also compare our methods with WAH, and the results are shown in Table 1 in the main paper. We observe that our method significantly outperforms all baselines measured by success rate with the fewest number of moves.

Q5:Does the proposed framework suffer from the large number of logic representations to be generated in the inference? If not, how does it avoid this problem? Are there any restrictions over the considered language/environments?

A5: Yes, the proposed framework suffers from the large number of logic representations to be generated. The best set of logic rules is approximately obtained by sampling and preserving the top-K rules according to their posterior probabilities. Note that in the supplementary material section 5, we have demonstrated the optimization of our proposed algorithm, which clearly describes the calculation of the posterior probabilities of the latent rule and the selection of high-quality rules from a large number of logic representations. This sampling strategy, which focuses on the most probable logic rules, allows our framework to operate efficiently without compromising the integrity of the inference process.

Q1:The definitions of entity, relation, and logic rule are inconsistent with the widely agreed definition in the knowledge graph academia.

A1: Thank you for your valuable suggestions. We clarify the differences in the definitions of entity and the relation between logic reasoning and knowledge graph reasoning as follows:

1. Definition of Entity

• In logical reasoning, an entity refers to an individual object or thing that exists in a domain of interest. Entities are typically represented by constants or variables in logical formulas or expressions. In this context, entities are often abstract and do not necessarily have any explicit semantic meaning. They serve as placeholders or representations for objects or concepts under consideration.

• In knowledge graph reasoning, an entity represents a specific object, concept, or instance in the real world. In a knowledge graph, entities are typically represented as nodes, and they can have attributes or properties associated with them. These entities are often grounded in real-world entities, such as persons, locations, or organizations.

• The main difference between entities in logic reasoning and those in knowledge graph reasoning lies in their representation and use within a system. In logical reasoning, entities are abstract and do not necessarily have a distinct correspondence to real-world objects, while entities in knowledge graphs are explicitly linked to real-world objects or concepts and are part of a larger interconnected structure.

2. Definition of Relation

• In logical reasoning, a relation represents a connection or association between entities. Relations are often represented by predicates or logical operators that indicate the relationship between the entities. These relations can be unary (relating an entity to itself), binary (relating two entities), or higher-order (relating multiple entities). Relations are often abstract and do not have explicit semantics.

• In knowledge graph reasoning, Relations are typically represented as edges connecting nodes in the graph. They have specific meanings associated with them, such as “is-a,” “part-of,” or “located-in.” Knowledge graph reasoning involves leveraging these semantic relationships to make inferences, perform queries, or discover new knowledge.

• The main difference is that relations in logical reasoning can have any number of entities, while relations in knowledge graph reasoning can only tolerate two entities because the unit of knowledge graph is the “Entity-Relation-Entity” triplets.

We have carefully reviewed the symbol definitions in the paper and distinguished them from the definitions in the knowledge graphs.

Q2:Different examples of rules are inconsistent.

A2:Thank you for your valuable feedback. In our setting, the command “Walk_to” needs a person as the first entity argument. We have rectified all ambiguous instructions in the paper.

Q3:minor errors.

A3: Following the reviewer’s suggestions, we have modified all tables and added arrows (↑ or ↓) next to each metric to indicate whether a higher or lower value is considered better. These modifications will help readers quickly identify the best results and understand the direction of improvement for each metric.

Q4:There are a few confusing wordings. What is the meaning of "hardness level" in the caption of Tab.1 and Tab.2? Its meaning is more like "non-softness" than "difficulty".

A4: We follow [1] to split our datasets into four hardness levels, and the gaps between levels correspond to different challenges. We apologize for any misunderstanding caused by the wording and make the necessary adjustments in the captions of Table 1 and Table 2 to ensure clarity and avoid any further confusion.

[1] Wan Y, Mao J, Tenenbaum J. HandMeThat: Human-Robot Communication in Physical and Social Environments[J]. Advances in Neural Information Processing Systems, 2022, 35: 12014-12026.

Q1: The experimental tasks seem somewhat weak.

A1:Thanks for your feedback. Following your suggestions, we consider incorporating additional robust human-AI collaboration tasks, including overcooked game [1], which is a benchmark environment for fully cooperative human-AI task performance. The goal of the game is to deliver soups as fast as possible. The agents should split up tasks on the fly and coordinate effectively in order to achieve high reward. The six possible actions are: up, down, left, right, noop, and "interact", which does something based on the tile the player is facing, e.g. placing an onion on a counter. Each layout has one or more onion dispensers and dish dispensers, which provide an unlimited supply of onions and dishes respectively. This game includes five layouts: Cramped Room, Asymmetric Advantages, Coordination Ring, Forced Coordination, and Counter Circuit. As good coordination between teammates is essential to achieve high returns in this environment, we use cumulative rewards over a horizon of 400 timesteps for our agents as a proxy for coordination ability. For all DRL experiments, we report average rewards across 100 rollouts and standard errors across 5 different seeds. We present quantitative results in these five layouts in the following table. There is a large gap between our method and Seq2Seq in all layouts. We will put these results into our revised manuscript.

Table1: Rewards over trajectories of 400 timesteps for our methods and Seq2Seq.

[1] Carroll M, Shah R, Ho M K, et al. On the utility of learning about humans for human-ai coordination[J]. Advances in neural information processing systems, 2019, 32.

Q2:The authors should provide the related work in the main text rather than in the appendix.

A2:Thanks for your recommendation. By highlighting the existing research and advancements in human-AI collaboration, we can demonstrate the significance of our work and the contributions we are making to this particular area. We have added related work that focuses on human-AI collaboration into our revised manuscript.

Q3: Presentation error.

A3: Thank you for your valuable suggestions. I have certainly incorporated your recommendations to improve the clarity and formatting of our paper.

Q4:Why does logical reasoning help enhance human-AI collaboration?

A4: Logical reasoning allows humans and AI systems to interpret and understand each other’s actions, intentions, and reasoning processes. By applying logical rules and principles, both parties can analyze and make sense of the information exchanged during collaboration. This shared understanding enables effective communication and coordination. It ensures coherence and consistency in the collaboration process. When humans and AI systems apply logical principles, they can identify and resolve contradictions or inconsistencies in their respective actions or decisions. This helps in aligning their efforts and maintaining a coherent and productive collaboration. By employing logical thinking, both humans and AI systems can break down complex problems into smaller components, identify patterns, and derive logical deductions to arrive at optimal solutions. We have added more analysis and reasoning experiments (e.g, overcooked games) in the supplementary material to elucidate the relationship between logical reasoning and human-AI collaboration.

Q1:The rule generator and the reasoning evaluator are important but don't show the particular design.

A1: In our original submission, because of the page limitation in the main paper, the design and hyper-parameters of the rule generator and the reasoning evaluator are described in the supplementary material Section 3, 4, 5 and 6. Below we show some description for the reviewer’s convenience (more details can be found in the supplementary material).

Rule Generator: We deploy Transformer-based framework to model the rule generator $p_{\theta}$. Specifically, we define the distribution of a set of rules as follows:

$

p_\theta(z \mid \mathbf{v}, \tau_t) = \Psi(z|N,\text{Trans}_{\theta}(\mathbf{v}, \tau_t)),

$

where $\Psi(\cdot)$ is multinomial distributions, $N$ is the number of the top rules, and $\text{Trans}_\theta(\mathbf{v}, \tau_t)$ defines a distribution over compositional rules with spatial-temporal states. The generative process of the rule set is quite intuitive, where we simply generate $N$ rules to form $z$.

Reasoning Evaluator: Suppose there is a rule set $F_{g}$, where the event $g$ is the head predicate (sub-goal). All the rules will play together to reason about the occurrence of $g$. For each $f \in F_{g}$, one can compute the features as above. Given the rule set $F_{g}$, we model the probability of the event $g$ as a log-linear function of the features. Here we assume the rule content is latent, and the rule evaluator is given as:

$

p_\alpha(g | \mathbf{v}, z, \tau_t) = \frac{\exp \left( \sum\nolimits_{f \in z_{g}} \alpha_{f} \cdot \phi_{f}(g| \mathbf{v}, \tau_t) \right)}{\sum_{g'}\exp \left( \sum\nolimits_{f \in z_{{g}'}} \alpha_{f} \cdot \phi_{f}({g}'| \mathbf{v}, \tau_t) \right)}.

$

Hyper-parameters: In the first stage, the input of our framework is the historical trajectory of entities, and the output is the generated logic rules. The historical trajectory would be first encoded into a scene graph and pass through three-layer MLPs before being fed into the transformer, and a ReLU non-linearity following each of the first two layers. In rule generator, the dimensions of keys, values, and queries are all set to 256, and the hidden dimension of feed-forward layers is 512. The number of heads for multi-head attention is 8.

In the second stage, the reasoning evaluator is also transformer-based architecture, where the dimensions of keys, values, and queries are all set to 256, the hidden dimension of feed-forward layers is 512, and the number of heads for multi-head attention is 8.

Q2:The Iterative Goal Inference seems that a process of conditional learning, so how to implement this part is not clear enough.

A2: Thanks for your suggestions. Iterative goal inference has been described in Section 2.4, and we make it detailed as follows:

Iterative goal inference is a method that employs the accumulated trajectory data to determine the robot’s most likely goal at any given moment. This process is mathematically represented by the equation $g^* = \arg\max_g p_\alpha(g | s^t, a_H^t, \tau^t)$, where $g^*$ is the inferred goal that maximizes the conditional probability based on the current state $s^t$, the action the human takes $a_{H}^t$ and the trajectory $\tau^t$. To implement Iterative Goal Inference in a practical setting, the robot continually updates its subgoals and beliefs. This is done by integrating the most recent observations and applying predefined logic rules. Such a mechanism permits the robot to craft and execute new plans in real time, thereby enhancing its collaborative capability with humans.

Through a continuous loop of inference based on current data and subsequent action, the robot can effectively align its behavior with human intentions and adapt to changing circumstances in a collaborative environment. Here's a more detailed breakdown of the process:

Observation Integration: At each step, the robot integrates new observational data, which includes the current state, human actions, and trajectory information.

Goal Inference: Using the probabilistic function, the robot infers the most probable goal at the current moment based on the integrated data.

Plan Formulation and Execution: With the inferred goal, the robot formulates a new plan that includes subgoal and action to be taken. It then executes this plan concurrently with the human, allowing for real-time collaborative adjustments.

This iterative process ensures that the robot's assistance is relevant, timely, and contextually appropriate, thereby providing effective support to the human collaborator.

Dear Reviewer,

I hope this message finds you well. We've made revisions based on your previous feedback and are keen to know if there are any remaining issues or further clarifications needed.

Your insights are very important to us, and we eagerly await your response.

Thank you for your time and effort.

Best regards,

The authors

Thank you for all your constructive comments! We wonder whether our response has addressed your major concerns to allow the paper to cross your acceptance threshold. Should there be any further specific issues you would like us to address, we welcome your input and are fully prepared to incorporate any additional modifications into the final version of our manuscript.