Concise and Organized Perception Facilitates Large Language Models for Deductive Reasoning

Thanks for your insightful feedback. We are encouraged that you find our paper valuable and each of your questions are discussed below.

Q1: What are the proofs generated by CoT are like? How does CoT concretely improve the proof planning of LLMs? It would be better if the authors could show some of the cases.

Response for Q1:

Thanks for the kind suggestion. We suppose that you are asking about how does COP rather than CoT improve the proof planning of LLMs. In some cases, LLMs with CoT based on the original context fail to find the optimal facts and rules to determine whether the given statement is True or False. In some other cases, LLMs with CoT can obtain the correct answer with incorrect reasoning chains. Due to the word limit, we show one case below.

Rules:

If someone eats the bear and the bear likes the cow then the bear likes the dog. If someone is kind then they chase the mouse. If someone eats the cow then the cow is young. If someone likes the mouse then they eat the dog. If the dog likes the mouse and the mouse does not like the dog then the mouse does not like the cow. If the cow is young and the bear does not chase the cow then the cow is kind. If someone eats the cow then the cow eats the mouse. If someone eats the dog then they eat the cow.

Facts:

The bear does not chase the cow. The bear is big. The bear is cold. The bear is young. The bear likes the dog. The bear likes the mouse. The cow does not chase the dog. The cow likes the mouse. The dog does not chase the bear. The dog does not eat the cow. The dog is not cold. The dog does not like the bear. The dog likes the cow. The dog does not like the mouse. The mouse is kind. The mouse likes the bear.

Question:

The cow is not young.

Context reconstructed by COP: The bear likes the mouse. The cow likes the mouse. If someone likes the mouse then they eat the dog. If someone eats the dog then they eat the cow. If someone eats the cow then the cow is young.

LLM’s proof steps produced by CoT based on the context reconstructed by COP: The bear likes the mouse. The cow likes the mouse. If someone likes the mouse then they eat the dog. Therefore the bear eats the dog and the cow eats the dog. If someone eats the dog then they eat the cow. Therefore the bear eats the cow and the cow eats the cow. If someone eats the cow then the cow is young. Therefore the cow is young. Therefore the given statement 'The cow is not young' is False.

LLM’s proof steps produced by CoT based on the original context: If the cow is not young, it means that someone has eaten the cow. According to Rule 6, if someone eats the cow, then the cow eats the mouse. However, based on the given facts, we know that the cow likes the mouse, which contradicts the statement. Therefore, the statement "The cow is not young" is False.

LLMs with CoT based on the original context can easily produce wrong answers or unfaithful proof steps, like “based on the given facts, we know that the cow likes the mouse, which contradicts the statement. ” in the above example. However, with the concise and organized context reconstructed by COP, LLMs with CoT is able to produce correct answer with faithful proof steps.

Q2: The experiments are conducted on three synthetical logical reasoning datasets. I wonder if this approach can be adapted to real-world data.

Response for Q2:

Yes, COP can be adapted to real-world data. To address this issue, we further conduct experiments on FOLIO, a real-world logical reasoning benchmark with various type of rules. To adapt to FOLIO, which is more complex and contains various language patterns and rule types, COP adopts a combination of rouge scores and semantic similarity method to generate the concept maps and mind maps. With the slight adjustment, COP outperforms CoT and LogicLM while LAMBADA is not able to work on this dataset, demonstrating the general efficacy of COP. The concise and organized context that COP provides on FOLIO facilitates the reasoning of LLMs while CoT still suffers from redundant and out-of-order context.

Thank you for your careful review. We carefully discuss all your concerns and questions below.

W1: The clarity of presentation can be significantly improved. I don't fully understand the method.

Response for W1:

Thanks for the suggestion. We have added a consistent example in the methodology part and make some revisions to improve the clarity.

A brief and more clear introduction of our method with a consistent running example

In this paper, we demonstrate that LLMs excel in deductive reasoning but struggle in proof planning. Therefore, we naturally come up with an idea to imitate of human cognition. The proposed COP first obtains a comprehensive understanding of the reasoning context by generating a concept map depicting the relevance between given rules and facts. Then, given a query that need to be proven or answered, COP identifies the most relevant information from the concept maps while eliminating redundancy, resulting in a mind map-like structure centered around the query node. After that, LLMs are prompted by the context sentences which are organized in a progressively ordered manner within one or more sequential sub-mind maps, in order to better adapt to the inference process of the model.

Given a context:

Rule1: All blue things are green. 

Rule2: All rough, nice things are young. 

Rule3: Green things are nice. 

Rule4: If Erin is blue and Erin is furry then Erin is rough. 

Rule5: Green, smart things are furry. 

Rule6: All furry things are blue.

Fact1: Bob is furry. 

Fact2: Bob is rough. 

Fact3: Erin is blue.

Fact4: Erin is furry. 

Fact5: Erin is green. 

Fact6: Erin is nice. 

Fact7: Erin is young.

The target is to prove whether it is True or False that Bob is nice.

Firstly, to imitate the process of human beings organizing thoughts, a concept map is generated to present the relevance of given rules and facts. The generation process further consists of two steps.

1. Simplified Representations of Rules and Facts. To enable connecting relevant rules and facts with each other, we utilize LLMs with few-shot prompt to create a unified and simplified representation for the facts and the rules. For example, Rule1 is changed into “conditions: [X(is, blue)], consequents: [X(is, green)] “where “X” can be substituted by any entities. Fact1 is changed into “[Bob(is, furry)]”.
2. Connecting of Rules and Facts. With the simplified representations of rules and facts, we connect each rule to facts as well as rules whose consequents satisfy one or more of the conditions specified in the current rule. For example, by unifying same entities, we can connect Rule1 to Fact3 since they share the same entity “blue”.

Secondly, given a query (i.e., Bob is nice in the given example), we identify relevant clues from the concept maps to create a mind map with the question node at its center. The process also consists of two sub steps.

1. Simplified Representation of the given question. Similar to the simplifying process of facts and rules, we utilize LLMs with few-shot prompt to change “Bob is nice” into “[Bob(is, nice)]” and its contrary statement “[Bob(is not, nice)]”.
2. Generation of the mind map. With the simplified question, we use the same way as we connect rules and facts when constructing the concept to identify the relevant rules and facts. For example, “Bob(is, nice)” can be connected by Rule3 (i.e., Green things are nice. ). Therefore, we are able to obtain a mind map by perform a D-depth searching starting from Rule3 in the concept map where D is the max reasoning depth. In this way, a number of irrelevant rules and facts can be excluded from the mind map.

The mind map might consists of several sub mind maps, each of which is a potentially possible reasoning path to determine whether the given question is True or False. Before we utilize LLMs to perform the final reasoning, we reconstruct the reasoning context in two steps:

1. Sub-Mind map Pruning. Since we know what to prove, we can remove sub mind maps which are obviously useless. Sub mind maps without a valid fact can not be used to reach a conclusion. Therefore, sub mind maps like “Rule5 -> Rule6 -> Rule1 -> Rule3” is removed.
2. Context Reconstruction. We reconstruct a reasoning context for each remaining sub-mind map. Given the sub mind map “Fact1 -> Rule6 -> Rule1 -> Rule3”, the context is reconstructed as “Bob is furry. All furry things are blue. All blue things are green. Green things are nice.” by traversing the sub-mind map from its leaf nodes to the root node which naturally adapts to the LLMs.

Finally, we use the reconstructed contexts to prompt the reasoning of LLMs until a true or false statement regarding the given question is made.

We hope that the statements above can improve the clarity.

Thanks for the thoughtful and constructive suggestions. We discuss each of them below and hope that the changes made can improve the clarity and significance of this work.

W1: The methodology part of the concept, mind graph generation, and mind graph pruning is a bit hard to read without a consistent running example and the prompt.

Response for W1:

Thanks for the kind suggestion. We have added a consistent running example as suggested and hope it can improve the clarity.

A brief and more clear introdution of our method with a consistent running example

In this paper, we demonstrate that LLMs excel in deductive reasoning but struggle in proof planning. Therefore, we natually come up with an idea to imitate of human cognition. The proposed COP first obtains a comprehensive understanding of the reasoning context by generating a concept map depicting the relevance between given rules and facts. Then, given a query that need to be proven or answered, COP identifies the most relevant information from the concept maps while eliminating redundancy, resulting in a mind map-like structure centered around the query node. After that, LLMs are prompted by the context sentences which are organized in a progressively ordered manner within one or more sequential sub-mind maps, in order to better adapt to the inference process of the model.

Given a context:

Rule1: All blue things are green. 

Rule2: All rough, nice things are young. 

Rule3: Green things are nice. 

Rule4: If Erin is blue and Erin is furry then Erin is rough. 

Rule5: Green, smart things are furry. 

Rule6: All furry things are blue.

Fact1: Bob is furry. 

Fact2: Bob is rough. 

Fact3: Erin is blue.

Fact4: Erin is furry. 

Fact5: Erin is green. 

Fact6: Erin is nice. 

Fact7: Erin is young.

The target is to prove whether it is True or False that Bob is nice.

Firstly, to imitate the process of human beings organizing thoughts, a concept map is generated to present the relevance of given rules and facts. The generation process further consists of two steps.

1. Simplified Representations of Rules and Facts. To enable connecting relevant rules and facts with each other, we utilize LLMs with few-shot prompt to create a unified and simplified representation for the facts and the rules. For example, Rule1 is changed into “conditions: [X(is, blue)], consequents: [X(is, green)] “where “X” can be substituted by any entities. Fact1 is changed into “[Bob(is, furry)]”.
2. Connecting of Rules and Facts. With the simplified representations of rules and facts, we connect each rule to facts as well as rules whose consequents satisfy one or more of the conditions specified in the current rule. For example, by unifying same entities, we can connect Rule1 to Fact3 since they share the same entity “blue”.

Secondly, given a query (i.e., Bob is nice in the given example), we identify relevant clues from the concept maps to create a mind map with the question node at its center. The process also consists of two sub steps.

1. Simplified Representation of the given question. Similar to the simplifying process of facts and rules, we utilize LLMs with few-shot prompt to change “Bob is nice” into “[Bob(is, nice)]” and its contrary statement “[Bob(is not, nice)]”.
2. Generation of the mind map. With the simplified question, we use the same way as we connect rules and facts when constructing the concept to identify the relevant rules and facts. For example, “Bob(is, nice)” can be connected by Rule3 (i.e., Green things are nice. ). Therefore, we are able to obtain a mind map by perform a D-depth searching starting from Rule3 in the concept map where D is the max reasoning depth. In this way, a number of irrelevant rules and facts can be excluded from the mind map.

The mind map might consists of several sub mind maps, each of which is a potentially possible reasoning path to determine whether the given question is True or False. Before we utlize LLMs to perform the final reasoning, we reconstruct the reasoning context in two steps:

1. Sub-Mind map Pruning. Since we know what to prove, we can remove sub mind maps which are obviously useless. Sub mind maps without a valid fact can not be used to reach a conclusion. Therefore, sub mind maps like “Rule5 -> Rule6 -> Rule1 -> Rule3” is removed.
2. Context Reconstruction. We reconstruct a reasoning context for each remaining sub-mind map. Given the sub mind map “Fact1 -> Rule6 -> Rule1 -> Rule3”, the context is reconstructed as “Bob is furry. All furry things are blue. All blue things are green. Green things are nice.” by traversing the sub-mind map from its leaf nodes to the root node which naturally adapts to the LLMs.

Finally, we use the reconstructed contexts to prompt the reasoning of LLMs until a true or false statement regarding the given question is made.

We hope that the above statements can improve the clarity.

After reading the author rebuttal, I am convinced by the new data and new story. I have raised my review score from 5 to 6.

Thanks for your valuable and insightful comments. We address the questions and concerns below.

W1: The paper seems to heavily build upon pre-existing methods such as "graph-based reasoning systems" and "structured knowledge integration," which have been extensively explored in the literature (e.g.,logical NNs and other neuro-symbolic approaches)

Response for W1:

We thank the reviewer for their valuable feedback and for raising their concerns regarding the potential reliance on pre-existing methods in our proposed approach. We appreciate the opportunity to address this issue.

We would like to emphasize the difference between our method and graph-based reasoning systems as well as neuro-symbolic approaches.

Features of Graph-based reasoning systems and Neuro-symbolic approaches

Graph-based reasoning systems typically represent knowledge and logical constraints explicitly as nodes and edges in a graph structure while neuro-symbolic approaches, Logic NNs for instance, generally translate logical operations such as AND, OR, and NOT into differentiable components that can be trained alongside neural network parameters. These methods perform reasoning relying on either the logical constraints contained in the graph structure or the trained logical components.

Difference with Graph-based reasoning systems and Neuro-symbolic approaches

While the generation of concept maps and mind maps in our method may appear similar to graph-based reasoning systems, we demonstrate notable differences between them in three key aspects.

Firstly, there are no logical operations involved during the generation of concept maps and mind maps. It is only a process to identify and organize relevant information. We leave all the reasoning part to LLMs.

Secondly, the concept maps and mind maps are not kept once a more organized and concise form of context is obtained. We leave all the reasoning part to LLMs and the processed context is the only input to LLMs. The reasoning process is not constrained by any graph structure or logical components.

Thirdly, our method can be seen as a new prompt engineering technique without altering the underlying model architecture or training paradigms like Logic NNs do.

Overall, by carefully adapting the given context to the inference process of LLMs in a concise and organized manner, we aim to lower the difficulty of proof planning for LLMs and unlock the deductive reasoning abilities that were previously untapped, while the generation of concept maps and mind maps in our method is just an approach to obtain a concise and organized context.

W2: The justification for why the combination of concise and organized strategies is more effective remains unclear under a rigorous theoretical framework. The examples provided (Sec 3 and Fig 3) do not offer evidence that this combination offers a qualitatively different approach to reasoning in LLMs as compared to existing methods.

Response for W2:

We would like to thank the reviewer for their valuable feedback and the opportunity to address their concern.

Why the combination of concise and organized strategies is more effective

Firstly, previous Literature [1] offers experimental evidence and states that the order of proofs affects reasoning.

Secondly, in this paper, we have conducted experiments in Figure 1 (d) to support our motivation. We randomly select 196 samples from the ProofWriter dataset and reconstruct the context based on the provided ground-truth proofs into either concise or organized forms while regarding the ground-truth proofs as concise and organized. The results in Figure 1(d) demonstrate that both organized and concise input context can greatly improve the reasoning accuracy of LLMs. The results also indicate the complementarity between concise and organized perception with the combination of them yields a relative performance improvement of over 100% (35.9% vs 71.9%) in a 5-hop setting. The reason why this combination can work might be that it greatly decreases the difficulty of proof planning which LLMs still struggle with.

[1] Abulhair Saparov and He He. Language models are greedy reasoners: A systematic formal analysis of chain-of-thought. In The Eleventh International Conference on Learning Representations, 2023