The Role of Deductive and Inductive Reasoning in Large Language Models

## Abstract

Abstract Large Language Models (LLMs) have achieved substantial progress in artificial intelligence, particularly in reasoning tasks. However, their reliance on static prompt structures, coupled with limited dynamic reasoning capabilities, often constrains their adaptability to complex and evolving problem spaces. In this paper, we propose the D eductive and I n D uctive( DID ) method, which enhances LLM reasoning by dynamically integrating both deductive and inductive reasoning within the prompt construction process. Drawing inspiration from cognitive science, the DID approach mirrors human adaptive reasoning mechanisms, offering a flexible framework that allows the model to adjust its reasoning pathways based on task context and performance. We empirically validate the efficacy of DID on established datasets such as AIW and MR-GSM8K, as well as on our custom dataset, Holiday Puzzle, which presents tasks about different holiday date calculating challenges. By leveraging DID’s hybrid prompt strategy, we demonstrate significant improvements in both solution accuracy and reasoning quality, achieved without imposing substantial computational overhead. Our findings suggest that DID provides a more robust and cognitively aligned framework for reasoning in LLMs, contributing to the development of advanced LLM-driven problem-solving strategies informed by cognitive science models.

## 1 Introduction

"The measure of intelligence is the ability to change." – Albert Einstein

Large Language Models (LLMs), such as GPT-4, have transformed natural language processing by excelling in tasks such as language translation, summarization, and question-answering (OpenAI, ), particularly in reasoning tasks and few-shot learning. However, there is ongoing debate regarding their problem-solving reliability. According to Zhou et al. (), scaling up and fine-tuning LLMs enhances their capabilities but also diminishes reliability, introducing unpredictable errors even in simple tasks and reducing the effectiveness of human supervision. Conversely, Li et al. () highlights that the application of the Chain of Thought (CoT) (Wei et al., ) methodology significantly improves the accuracy of LLMs in arithmetic and symbolic reasoning tasks by enabling inherently serial computations, which pose challenges for low-depth transformers. Furthermore, Bubeck et al. () observes that LLMs demonstrate a high degree of accuracy and consistency in multi-step reasoning tasks, particularly when employing techniques such as CoT and self-consistency (Wang et al., ). Additionally, reinforcement learning from human feedback (RLHF) has been shown to enhance model performance, notably reducing the incidence of harmful or inaccurate outputs (Ouyang et al., ; Christiano et al., ). These insights suggest that, despite concerns related to model scalability and the potential for errors introduced during fine-tuning (Zhou et al., ), LLMs can exhibit considerable reliability in complex reasoning tasks when guided by structured methodologies and reinforced with human feedback. Ensuring the robustness of LLM outputs remains a critical priority, necessitating further investigation into strategies

Figure: Figure 1: Comparison of reasoning approaches in LLMs including the IO, CoT, and DID framework, highlighting the progression from direct output generation to dynamic inductive and deductive reasoning for more adaptive problem-solving.
Refer to caption: x1.png

aimed at enhancing model resilience and dependability.

Despite the notable success of LLMs, they face several limitations when dealing with more complex and evolving tasks. In particular, their rigidity in reasoning and difficulty in generalizing across diverse problem types present significant challenges. A key limitation of current LLMs is their reliance on static prompt structures and patterns learned during training, which restricts their adaptability in novel or evolving contexts. These models often apply fixed strategies to problem-solving(Shi et al., ; Li, ),
leading to challenges in tasks that require logical reasoning, such as calculating family relationships, performing numerical comparisons, or counting specific characters in a word (Nezhurina et al., ). Although these tasks may seem straightforward, LLMs tend to depend on pre-learned patterns instead of dynamically adjusting their reasoning processes, resulting in errors in more complex problem spaces (Marcus, ; Hendrycks et al., ). This inflexibility contrasts with human problem-solving, which is typically iterative and adaptive (Sloman, ). Humans use inductive reasoning to derive general rules from specific instances and then apply deductive reasoning to novel situations, allowing for dynamic strategy adjustments based on task complexity. In contrast, current LLMs lack this level of flexibility in reasoning, which limits their ability to generalize and adapt to more sophisticated scenarios. This underscores the need for increased attention and research in this area.

Moreover, LLMs have difficulty generalizing reasoning across tasks that require dynamic adjustment or incremental problem-solving. While LLMs can achieve high accuracy on specific tasks, their performance often degrades when confronted with problems that evolve or require multi-step reasoning. This issue is especially evident in tasks where the model must balance different reasoning strategies or integrate information from multiple sources. Tasks such as stepwise numerical reasoning, temporal reasoning, or complex multi-step inference highlight gaps in LLMs’ ability to maintain consistent reasoning across different stages of a task. These models tend to produce inconsistent or contextually inappropriate answers when required to adjust their reasoning dynamically as the problem unfolds. The static and inflexible nature of their reasoning pipeline limits generalization and accuracy, particularly when compared to human problem-solving, which adapts to new information in real-time. Despite improvements with techniques like CoT (Wei et al., ), Tree-of-Thought (ToT) (Yao et al., ), Temperature-Tree-of-Thought (T^2oT) (Cai et al., ), and Graph-of-Thought (GoT) prompting (Besta et al., ), current LLMs still struggle to adjust their reasoning dynamically, resulting in difficulties in addressing more fluid and complex tasks.

To address these challenges, we propose the De-In-Ductive (DID) method, a novel approach designed to enhance LLM reasoning by integrating both inductive and deductive reasoning processes within the prompt construction framework as the Figure 1 shows. Grounded in cognitive science models of human reasoning, the DID method enables LLMs to adjust their reasoning pathways dynamically in response to the task context and its evolving complexity. In the DID method, inductive reasoning is first used to derive general rules from specific instances, followed by deductive reasoning to apply these rules in solving particular problems. This hybrid reasoning process mirrors human cognitive strategies, allowing the model to adjust its reasoning dynamically based on real-time feedback. By employing this dynamic prompt strategy, the DID method improves the adaptability and flexibility of LLMs, enabling them to better handle complex, evolving problem spaces.

We validate the effectiveness of the DID method on established benchmarks such as AIW and MR-GSM8K (Wei et al., ; Cobbe et al., ), as well as our custom dataset, Holiday Puzzle, which includes tasks about holiday date calculations. By leveraging DID’s hybrid prompt strategy, we observe significant improvements in both solution accuracy and reasoning quality, achieved without imposing substantial computational overhead. These results demonstrate the efficacy of DID in addressing the limitations of current LLM approaches. This work provides the following key contributions:

- •
We introduce a De-In-Ductive (DID) methodology that integrates both inductive and deductive reasoning within LLM prompt construction. This dynamic approach addresses key limitations of static prompt structures, enhancing the model’s reasoning flexibility and adaptability.
- •
Through empirical evaluations, we demonstrate that the DID method significantly enhances the adaptability and efficiency of LLMs across a diverse set of complex tasks. Moreover, DID improves solution accuracy and reasoning quality without incurring substantial computational overhead.

## 2 Related Works

#### Cognitive Science and Deductive-Inductive Reasoning

Deductive and inductive reasoning are foundational concepts in cognitive science for understanding human thought processes. Deductive reasoning, formalized by philosophers like Kant, involves applying general principles to specific cases, ensuring conclusions logically follow from premises. Inductive reasoning, conversely, generalizes from specific observations to form broader conclusions, as highlighted in The Riddle of Induction (Goodman, ). Cognitive models view these modes of reasoning as complementary, where inductive reasoning generates hypotheses, and deductive reasoning tests them (Wason, ). The interplay between these two reasoning methods has been shown to enhance problem-solving accuracy, particularly in uncertain domains where balancing exploration and validation is critical (Johnson-Laird, ; Tversky & Kahneman, ). Research on mental models and heuristics highlights how this dynamic combination allows for more flexible reasoning, especially in tasks characterized by complexity or ambiguity. Problems in cognitive science are often classified based on their structure and uncertainty: well-structured problems (e.g., mathematical proofs) lend themselves to deductive reasoning, whereas ill-structured or open-ended problems (e.g., scientific discovery) require inductive reasoning to form plausible hypotheses from incomplete data (Funke, ). Cognitive insights have been increasingly integrated into neural networks (L Griffiths et al., ), with recent studies emphasizing the importance of embedding inductive structures within models to improve generalization across tasks (Tenenbaum et al., ). The DID framework builds on this cognitive science foundation by dynamically combining inductive and deductive reasoning within LLMs, creating a hybrid model that mirrors human cognitive processes and enhances adaptability in problem-solving.

#### LLMs for Reasoning and Prompting Techniques

While LLMs like GPT-4 have shown remarkable capabilities in tasks such as text generation and summarization (Brown et al., ), they often struggle with structured reasoning, particularly in tasks involving logical inference, numerical comparison, and complex deduction (OpenAI, ; Nezhurina et al., ). These shortcomings have been well-documented in challenges like the ARC Prize (Rae et al., ) and in tasks that require step-by-step reasoning or multi-hop inferences. To address these limitations, prompting techniques such as CoT prompting (Wei et al., ),ToT (Yao et al., ), and GoT (Besta et al., ) have been developed to improve LLMs’ capacity for structured reasoning. CoT enhances stepwise reasoning by breaking down complex problems, while ToT and GoT explore multiple solution paths through structured thought representations. However, these approaches remain static, requiring extensive prompt engineering and lacking the dynamic adaptability needed for diverse tasks. Recent work, such as Hypergraph of Thoughts (HoT) (Yao et al., ), extends these methods to multimodal and more complex reasoning but still fails to offer the real-time adaptability needed for nuanced problem-solving. Another critical analysis by Marcus () highlights the limitations of current LLMs, emphasizing their struggles with maintaining logical consistency and coherence in complex reasoning tasks. The DID framework addresses these gaps by dynamically integrating inductive and deductive reasoning, making the reasoning process more adaptive and context-sensitive, informed by the probabilistic reasoning advancements seen in the combination of Bayesian models with neural networks (Gershman et al., ).

## 3 Methodology

The De-In-Ductive (DID) framework dynamically integrates inductive and deductive reasoning, inspired by cognitive science models of human reasoning. It balances inductive hypothesis generation and deductive rule application to improve the flexibility and adaptability of large language models (LLMs) in complex problem-solving tasks.

### 3.1 Preliminary

In this section, we formalize the core assumptions underlying the DID framework, which define the problem space and establish the performance limitations of LLMs in solving these problems. These assumptions lay the theoretical groundwork for modeling the interaction between problem complexity and the reasoning capabilities of LLMs.

#### Assumption 1 (Problem Distribution and Complexity)

Let $\mathcal{P}$ denote a problem space, where each problem instance $p\in\mathcal{P}$ is associated with an observed dataset $D_{p}=\{d_{1},d_{2},\dots,d_{n}\}$ and additional new data $D_{\text{new},p}=\{d_{1}^{\prime},d_{2}^{\prime},\dots,d_{m}^{\prime}\}$. Each problem $p$ is governed by a true underlying hypothesis $H_{p}$, which explains the relationship between the data and the problem context.

The observed data $D_{p}$ follows a joint distribution conditioned on the hypothesis $H_{p}$:

$$ $P(D_{p}\mid H_{p})=\prod_{i=1}^{n}P(d_{i}\mid H_{p}),$ (1) $$

where $d_{i}$ is independently generated according to the true hypothesis $H_{p}$. During the deductive phase, the model tests a candidate hypothesis $H$ against the new data $D_{\text{new},p}$, and the likelihood is given by:

$$ $P(D_{\text{new},p}\mid H)=\prod_{j=1}^{m}P(d_{j}^{\prime}\mid H).$ (2) $$

The complexity of each problem $p$ is characterized by a parameter $c(p)\in\mathbb{R}_{+}$, where higher values of $c(p)$ indicate more complex problems, influencing the difficulty of hypothesis testing and data modeling.

#### Assumption 2 (Baseline Performance and Deductive Probability)

Let $\mathcal{M}_{\text{LLM}}$ represent a baseline LLM with parameters $\theta$. For problems with complexity $c(p)\geq c_{0}$, the likelihood that $\mathcal{M}_{\text{LLM}}$ produces a correct solution is bounded by:

$$ $\mathbb{P}_{\text{correct}}(p,\theta)\leq\epsilon,\quad\text{for }c(p)\geq c_{ 0},$ (3) $$

where $\epsilon\ll 1$ reflects the baseline model’s limitations on novel or complex tasks.

During the deductive reasoning phase, the likelihood that the hypothesis $H$ holds, given the new data $D_{\text{new}}$, is computed by:

$$ $P_{\text{deductive}}(H\mid D_{\text{new}})=\prod_{i=1}^{m}P(d_{i}^{\prime}\mid H ,\theta),$ (4) $$

where the model tests the validity of $H$ using the new observations $D_{\text{new}}$ and adjusts its confidence in the hypothesis.

### 3.2 De-In-Ductive (DID) Framework

Figure: Figure 2: Comparison of reasoning approaches in Large Language Models (LLMs) including the IO method, Chain of Thought (CoT) prompting, and the De-In-Ductive (DID) framework, highlighting the progression from direct output generation to dynamic inductive and deductive reasoning for more adaptive problem-solving.
Refer to caption: x2.png

Figure 2 illustrates the comparison between the IO, CoT, and DID frameworks. The IO (Input-Output) Method processes natural language queries by retrieving patterns and facts without engaging in iterative reasoning. The Chain of Thought (CoT) Method improves logical reasoning by breaking down complex problems into sequential steps. Our proposed De-In-Ductive (DID) Method goes further by dynamically integrating inductive and deductive reasoning. By iteratively generating and testing hypotheses, DID adapts to problem complexities more effectively than static methods like CoT, optimizing problem-solving by balancing reasoning modes in response to task difficulty. Based on Assumptions  3.1 and  3.1, DID optimizes an objective function that balances both reasoning modes, dynamically adjusting as the complexity of the problem increases.

#### Inductive Reasoning

The inductive phase generates hypotheses from observed data $D_{p}$. Using Bayesian inference, the posterior probability for a hypothesis $H$ is calculated as:

$$ $P(H\mid D_{p})=\frac{P(D_{p}\mid H)P(H)}{P(D_{p})},$ (5) $$

where $P(H)$ is the prior probability and $P(D_{p}\mid H)$ is the likelihood of the observed data under hypothesis $H$.

#### Deductive Reasoning

In the deductive phase, the generated hypothesis $H$ is tested against the new data $D_{\text{new},p}$. The likelihood of the new data given the hypothesis is:

$$ $P(D_{\text{new}}\mid H)=\prod_{j=1}^{m}P(d_{j}^{\prime}\mid H).$ (6) $$

This phase refines the hypothesis by comparing how well it explains the new observations.

#### Hybrid Objective Function

The DID framework minimizes a hybrid objective function that integrates both inductive and deductive reasoning losses. The total objective function is defined as:

$$ $\mathcal{L}_{\text{DID}}(\theta)=\alpha\cdot\mathcal{L}_{\text{inductive}}( \theta)+(1-\alpha)\cdot\mathcal{L}_{\text{deductive}}(\theta),$ (7) $$

where $\mathcal{L}_{\text{inductive}}(\theta)$ represents the error in generalizing from the data, and $\mathcal{L}_{\text{deductive}}(\theta)$ penalizes errors in applying the rules to new instances. The weighting factor $\alpha$ adjusts dynamically based on the task complexity and the relative uncertainties in the inductive and deductive phases.

#### Dynamic Adjustment

The balance between inductive and deductive reasoning is dynamically weighted based on the uncertainties in each reasoning process:

$$ $\alpha_{t}=\frac{\mathbb{E}_{H}[P_{\text{inductive}}(H\mid D_{p})]}{\mathbb{E} _{H}[P_{\text{inductive}}(H\mid D_{p})]+\mathbb{E}_{D_{\text{new}}}[P_{\text{ deductive}}(D_{\text{new}}\mid H)]}.$ (8) $$

This adaptive mechanism ensures that DID can adjust its strategy according to the evolving complexity of the problem.

#### Limitations of Chain-of-Thought (CoT) under Assumptions

Under Assumptions 1 and 2, we infer that static reasoning methods such as Chain-of-Thought (CoT) prompting are insufficient for solving problems from the novel distribution $\mathcal{P}$. Since CoT relies on pre-learned patterns and fixed reasoning pathways, it lacks the dynamic adaptability required to handle new and complex problem structures. Specifically, without the ability to adjust $\alpha$ dynamically and integrate inductive hypothesis generation, CoT cannot effectively improve the low baseline performance ($\mathbb{P}(\text{Correct}\mid p,\theta)\leq\epsilon$) for complex problems.

#### Computational Complexity

The computational complexity of the DID algorithm can be expressed as $O(T\cdot(n_{\text{ind}}+n_{\text{ded}}))$, where $T$ is the number of iterations, $n_{\text{ind}}$ is the complexity of inductive reasoning per iteration, and $n_{\text{ded}}$ is the complexity of deductive reasoning per iteration. The dynamic adjustment enabled by the DID framework, as necessitated by Assumptions 1 and 2, reduces error propagation compared to static methods like CoT, thus improving efficiency and accuracy.

#### Efficiency Gains

By dynamically adjusting reasoning pathways according to task complexity and problem novelty, DID reduces the number of iterations required to converge on a solution. This adaptive process ensures that DID outperforms static methods like CoT in both performance and computational overhead, achieving higher accuracy with fewer computational resources.

#### Theoretical adaption analysis

The DID framework effectively manages cognitive load by initially focusing on simplified problem versions, allowing the model to concentrate on essential elements before engaging with more complex interactions. Through the inductive phase, the model observes specific instances, forming a foundation for generalization. As task complexity increases, the model transitions to deductive reasoning, applying generalized rules to arrive at a solution. This dynamic adjustment of reasoning strategies based on evolving task contexts enhances the model’s adaptability and problem-solving efficiency.

#### Integration with Existing Models

The De-In-Ductive (DID) method is compatible with various LLM architectures and can be seamlessly integrated with existing techniques such as CoT prompting (Wei et al., ). By providing a structured reasoning framework that dynamically incorporates both inductive and deductive reasoning, DID complements these methods and enhances the model’s problem-solving capabilities. Specifically, it structures the problem-solving process to allow for the dynamic integration of reasoning strategies, utilizes a structured template prompt that guides the model through incremental reasoning stages and improves adaptability and problem-solving efficiency without introducing significant computational overhead. By mirroring human adaptive reasoning processes, the DID method provides a more flexible and robust framework for LLMs to tackle complex and evolving problems.

## 4 Experiments

**Table 1: Merged Results for GPT-3.5 Turbo, GPT-4o, and Claude 3.5 Sonnet across Different Tasks (Alice Problem, MR-GSM8K, Holiday Puzzle)**
|  | Alice Problem | MR-GSM8K | Holiday Puzzle |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Model\Prompt Method | IO (%) | CoT (%) | DID (%) | CoT (%) | DID (%) | IO (%) | CoT (%) | DID (%) |
| GPT-3.5 Turbo | 6.7 | 8.6 | 13.3 | 68.1 | 73.3 | 0.2 | 1.4 | 5.6 |
| GPT-4o | 43.4 | 55.9 | 70.3 | 82.0 | 83.7 | 7.8 | 5.2 | 15.4 |
| Claude 3.5 Sonnet | 74.8 | 83.7 | 89.5 | 91.3 | 92.0 | 17.4 | 17.8 | 24.5 |

### 4.1 Alice problems

#### Task.

The AIW dataset is focused on evaluating the logical reasoning and deduction abilities of large language models (LLMs). The problems are structured around scenarios where models must infer relationships between family members based on a set of constraints, typically involving siblings, with questions like determining how many sisters or brothers a particular sibling has. Due to the AIW GitHub open-source dataset being provided in the form of questions and various prompts, we manually removed all prompts and eliminated duplicate questions that remained after prompt removal. This resulted in 113 unique original Alice problems. All subsequent experiments are based on these 113 problems, with results averaged over 20 runs.

#### Baseline and Framework Setup.

We compare the performance of the DID framework with three other prompting methods: the IO prompt (which directly utilizes the LLM without structured prompting) and the CoT prompt. All methods are evaluated in a zero-shot setting. The comparisons are performed using three representative models: GPT-4o, GPT-3.5-turbo, and Claude 3.5 Sonnet. GPT-4o was selected due to its highest reported accuracy in the AIW paper, while Claude 3.5 Sonnet achieved the second-highest accuracy. GPT-3.5-turbo, by contrast, demonstrated mid-to-low accuracy. For a fair comparison, all model parameters, including temperature, top-k sampling, and other hyperparameters, are maintained at their default values.

Figure: Figure 3: Comparison of reasoning approaches in Large Language Models (LLMs) including the IO method, Chain of Thought (CoT) prompting, and the De-In-Ductive (DID) framework, highlighting the progression from direct output generation to dynamic inductive and deductive reasoning for more adaptive problem-solving.
Refer to caption: x3.png

#### Results

The results in 1 present a comparative analysis of the IO, CoT, and DID prompting methods across three representative models: GPT-3.5 Turbo, GPT-4o, and Claude 3.5 Sonnet. Across all models, the DID framework consistently outperforms both IO and CoT methods, demonstrating its superior capability in handling multi-step reasoning tasks.

For GPT-3.5 Turbo, the DID method achieves an accuracy of 13.27%, significantly outperforming the IO prompt (6.73%) and CoT prompt (8.62%). This result highlights the DID framework’s ability to guide the model through structured, step-by-step reasoning, even in less powerful models like GPT-3.5 Turbo. Traditional prompt methods, such as IO and CoT, tend to struggle with multi-step reasoning because they either rely on direct output generation or follow static, predefined thought chains that lack the flexibility to adapt to more complex scenarios. On GPT-4o, the DID method reaches 70.27%, which far exceeds both IO (43.36%) and CoT (55.85%). The substantial margin between DID and other methods demonstrates its efficacy in managing logical deductions, particularly in more complex reasoning tasks. In contrast, the static nature of IO and the limited flexibility of CoT prevent these methods from fully addressing the intricacies of multi-step deductions. Claude 3.5 Sonnet exhibits the highest overall performance across all methods, with the DID method achieving an impressive accuracy of 89.49%, further extending its lead over IO (74.77%) and CoT (83.68%).

As illustrated in Figure 3, the DID framework excels in progressively guiding LLMs through increasingly complex reasoning steps, especially in tasks where relationships must be deduced from ambiguous information, such as determining family connections. Traditional prompt methods often fail to handle such tasks effectively because they attempt to solve the original complex problem directly, which can result in the model missing critical logical connections. This frequently leads to incorrect conclusions. By breaking down multi-step reasoning problems into simpler subproblems, the DID method ensures that the model remains on track and avoids common pitfalls. This structured approach enables LLMs to generalize effectively and handle more sophisticated logical problems, like those presented in the Alice problem.

### 4.2 MR-GSM8K math problems

#### Task.

MR-GSM8K builds upon the GSM8K benchmark but introduces significantly higher complexity by focusing on meta-reasoning. Since MR-GSM8K not only challenges models to identify and explain errors in provided solutions, but also making it more suitable for assessing the advanced cognitive abilities of LLMs. Only the dataset portion of MR-GSM8K is used, in order to test different methods. And the assessing portion is not used. The dataset includes harder problem types, such as reversed reasoning and programmatic thinking, requiring deeper understanding and reasoning capabilities, thus offering a more rigorous evaluation framework for state-of-the-art models.

#### Baseline and Framework Setup.

We compare the performance of the DID framework with the CoT prompt. The CoT is widely used as a method for improving the performance of LLM. All model parameters, including temperature, top-k sampling, and other hyperparameters, are set to their default values for a fair comparison.

#### Results

Based on the results shown in 1, the performance comparison across different models (GPT-3.5 Turbo, GPT-4o, and Claude 3.5 Sonnet) for the CoT and DID frameworks reveals the consistent superiority of the DID framework. On GPT-3.5 Turbo, the DID method achieves an accuracy of 73.3%, outperforming CoT (68.1%). Similarly, on GPT-4o, the DID method demonstrates a clear advantage with an accuracy of 83.7%, compared to 82.0% for CoT. For Claude 3.5 Sonnet, the DID method further solidifies its dominance, achieving an accuracy of 92.0%, surpassing CoT (91.3%). This consistent performance across models highlights the effectiveness of the DID approach.

In summary, across GPT-3.5 Turbo, GPT-4o, and Claude 3.5 Sonnet, the DID framework consistently outperforms the CoT framework in terms of accuracy, demonstrating a significant performance advantage. This consistent superiority suggests that the DID method possesses stronger reasoning capabilities and higher reliability for handling complex tasks.

### 4.3 Holiday Puzzle

#### Task.

The Holiday Puzzle is a task designed to evaluate the reasoning ability of LLMs in handling holiday arrangements. This task includes 20 examples, each based on a holiday and compensatory workday records from the past decade. The task requires the LLMs to calculate the actual number of extra holiday days people receive, excluding weekends that were already scheduled as rest days.

Figure: Figure 4: Comparison of reasoning approaches in Large Language Models (LLMs) including the IO method, Chain of Thought (CoT) prompting, and the De-In-Ductive (DID) framework, highlighting the progression from direct output generation to dynamic inductive and deductive reasoning for more adaptive problem-solving.
Refer to caption: x4.png

#### Baseline and Framework Setup.

To assess the effectiveness of the DID framework on the holiday calculation problem, we compare it with two alternative prompting methods: the IO prompt (which directly utilizes the LLM without structured prompting) and the CoT prompt.
For fairness, all model parameters, including temperature, top-k sampling, and other hyperparameters, are kept at their default values.

#### Results

As shown in 1, the performance comparison across different prompting methods (IO, CoT, and DID) on the "Holiday Puzzle" task highlights the consistent superiority of the DID framework. On GPT-3.5 Turbo, the DID method achieves an accuracy of 5.6%, significantly outperforming IO (0.2%) and CoT (1.4%). This demonstrates that even on less powerful models, the DID framework effectively helps capture the underlying structure of complex temporal and scheduling relationships. Similarly, on GPT-4o, the DID method shows a clear advantage, with an accuracy of 15.4%, compared to 7.8% for IO and 5.2% for CoT. For Claude 3.5 Sonnet, the DID method solidifies its dominance with an accuracy of 24.5%, far surpassing IO (17.4%) and CoT (17.8%).

In this task, the DID framework’s stepwise combination of inductive and deductive reasoning proves especially effective for capturing complex patterns such as the relationship Holiday rest days = Total rest days - Weekend rest days. Figure 4 demonstrates how DID enables the model to approach this problem systematically, avoiding the risk of falling into incorrect reasoning paths common in traditional prompt methods. By starting with simpler, deductively generated subproblems, the DID framework ensures that the model can handle both the intricacies of date calculations and generalize across varying input conditions. This step-by-step approach allows LLMs to refine their reasoning process as complexity increases, ultimately improving their overall accuracy on tasks like the Holiday Puzzle.

## 5 Discussion

### 5.1 Challenges of Achieving 100% Accuracy in Simple Tasks

Despite the implementation of advanced prompting techniques such as CoT, ToT, and our proposed DID method, LLMs continue to face challenges in consistently achieving 100% accuracy, even on seemingly simple logical tasks. A key factor underlying this limitation may be the fundamental architecture of LLMs. These models rely on predicting the next token in a sequence, which restricts their ability to maintain a coherent internal representation across multiple reasoning steps. While attention mechanisms allow models to reference previous tokens, they lack the robust cognitive structures that humans use to ensure logical integrity across reasoning processes. Consequently, LLMs can lose track of intermediate steps or overlook crucial logical connections, leading to errors in tasks that might otherwise appear straightforward. This token-based, output-driven mechanism, although effective in many natural language processing tasks, is inherently unsuited for tasks that require rigorous logical consistency and structured reasoning, explaining the persistence of basic mistakes in LLM outputs.

### 5.2 Fine-tuning LLMs with Deductive and Inductive Reasoning

The DID method proposed in this paper primarily focuses on prompting strategies without altering the underlying architecture or fine-tuning the LLM itself. However, future work could investigate the benefits of fine-tuning LLMs on datasets explicitly incorporating deductive and inductive reasoning processes. Fine-tuning strategies such as Reinforcement Learning from Human Feedback (RLHF), Retrieval-Augmented Generation (RAG), or other methods (Lewis et al., ; Ouyang et al., ; Christiano et al., ) could enhance the model’s ability to handle complex reasoning tasks. By integrating examples that demonstrate dynamic reasoning adjustments—similar to the DID approach—during the fine-tuning phase, models would gain a deeper understanding of inductive and deductive reasoning patterns. Additionally, emerging techniques like Test-Time Training (TTT) (Sun et al., ) could be explored to further improve models’ adaptability and reasoning performance during evaluation. These advancements are likely to enhance the consistency and reliability of LLM outputs in structured reasoning tasks by fostering more robust internal representations of logical thought processes.

### 5.3 The ARC Prize Challenge

The ARC (Abstraction and Reasoning Corpus) Prize represents a particularly challenging benchmark designed to evaluate an AI’s capacity for abstract reasoning and generalization. Unlike conventional AI tasks that target pattern recognition based on fixed datasets, ARC tests a model’s ability to generalize across diverse problem types, making it an ideal platform to assess the adaptability of frameworks such as our De-In-Ductive (DID) method. ARC problems require abstract reasoning across domains like visual pattern recognition and symbolic problem-solving—areas where DID’s integration of inductive and deductive reasoning could provide a competitive edge. The DID framework’s ability to adapt dynamically based on task complexity, first using inductive reasoning to hypothesize patterns and then applying deductive logic to test them, positions it well for tasks in the ARC benchmark. Given that ARC problems often involve iterative problem-solving and the ability to generalize from minimal examples, we believe the DID method is particularly suited for this task. Future work will focus on evaluating DID’s performance on ARC Prize tasks to test its robustness and effectiveness in abstract reasoning scenarios.

## 6 Conclusion

In this work, we introduced the De-In-Ductive (DID) method, a novel framework that dynamically integrates inductive and deductive reasoning to enhance the adaptability and reasoning capabilities of Large Language Models (LLMs). By leveraging cognitive science principles, the DID framework allows LLMs to evolve their problem-solving strategies in response to task complexity, overcoming the rigidity of static prompt structures. Through extensive empirical validation on both standard benchmarks and our custom Holiday Puzzle dataset, we demonstrated significant improvements in accuracy and reasoning quality, achieved without excessive computational costs. However, while DID advances the field, challenges remain in making LLMs more intelligent, particularly in ensuring better generalization to unseen tasks, maintaining adaptability in complex multi-step reasoning, and further refining model biases. Future research must continue to address these issues, paving the way for more robust and cognitively aligned artificial intelligence systems.

## Peer Reviews

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: Could the authors provide the exact structure of the DID prompts used in experiments?

What steps would be needed to make the experiments reproducible, such as providing the Holiday Puzzle dataset and detailed experimental setup?

Could the authors evaluated against methods like ToT, T2oT, and GoT that were mentioned in the paper?
soundness: 2
strengths: Originality: The DID framework’s combination of inductive and deductive reasoning is an interesting approach to enhancing reasoning flexibility.
summary: This paper presents the De-In-Ductive (DID) prompt strategy, which integrates deductive and inductive reasoning to improve adaptability in large language models (LLMs) for complex reasoning tasks. The DID approach, inspired by cognitive science, dynamically balances inductive hypothesis generation and deductive rule application, allowing models to adjust their reasoning pathways based on task complexity. Empirical validation across benchmark datasets (AIW, MR-GSM8K) and a custom dataset, Holiday Puzzle, highlights reported improvements in solution accuracy and reasoning quality without substantial computational overhead. By combining deductive and inductive reasoning, DID aims to enhance LLM performance in dynamic problem spaces.
weaknesses: Clarity of Figures and Descriptions: Some figures (e.g. 1, 4) lack essential information, such as dataset details, metric explanations, and setup descriptions, making it difficult to interpret results.

Prompt Strategy Details: As a prompt strategy paper, the DID method should explicitly define its prompt strategy. Currently, the methodology is insufficiently explained, with few details about how the DID prompts are structured or adapted dynamically.

Reproducibility: The paper lacks reproducibility; results, dataset (Holiday Puzzle), and other experimental resources are not attached.

Baseline Comparisons: Other prompting methods (ToT, T2oT, GoT) are mentioned but not evaluated against, which reduces the paper’s comparative validity.

ARC Challenge Reference: While the DID method is positioned as a potential solution for the ARC Prize Challenge, this claim is not backed by any testing on the ARC tasks, diminishing the value of this comparison.

---

confidence: 3
contribution: 2
initial_rating: 3
presentation: 1
questions: 1. Can the authors compare against more relevant baselines including ToT, and possible SoTA methods like o1?
2. AN understanding of how hypothesis can be improved and tailored to the task would be benefical to the application. Can the authors discuss this in more detail as it is central to their paper?
soundness: 2
strengths: 1. Flexible approach: While the approach is not entirely novel, it does appear more flexible than existing methods.
2. Improved accuracy: The authors demonstrate emperically that DID method somewhat outperforms the existing CoT methods.
summary: This paper attempts to introduce a novel approach called DID that uses deduction and induction to solve problems requiring reasoning.
weaknesses: 1. The paper does not contrast this approach with Tree of Thought approaches, or other methods that trade accuracy for inference timesteps. The shown baselines are quite weak and stale at this point in the field.

2. The problems being attacked by this paper would benefit significantly from tool use, which is not a mainstay of the paper. This lack of treatment reduces the impact and novelty of this method.

3. The paper's writing style can be improved to get to the core of the training methodology more quickly. The current structure requires readers to sift through substantial text before reaching key contributions.

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confidence: 3
contribution: 1
initial_rating: 3
presentation: 2
questions: 1) What is formally the hypothesis H_p? What is the hypothesis space? How the best H is chosen? How does it scale?
2) What is c_0 (eq 3)? It is undefined.
3) What is meant by "new data"? You mean the original available data are split into two different sets, like train and validation, and then used both for the inductive/deductive losses? I don't see otherwise how new (unlabelled/test) data could be used in Eq. 7.
4) How Eq. 8 has been chosen? This means you need to calculate \alpha_t any time a new data is considered?
5) What is the metric reported in Table 1? What is the variance over the 20 runs?
6) What is the role of Eq. 7 as experiments are considered in the zero-shot setting? Also, how the dynamic of data is modeled in the experiments?
soundness: 2
strengths: - Integrating both inductive and deductive reasoning within LLM is a very interesting challenge.
summary: This paper introduces the Deductive and InDuctive(DID) method, which enhances LLM reasoning by dynamically integrating both deductive and inductive reasoning within the prompt construction process. The method is shown to improve over both accuracy and reasoning capabilities on different datasets, without affecting significantly the computational cost.
weaknesses: - The introduction is quite long and I think it could be reduced to leave more space to more meaningful details about the method and the experiments.
- The description of the assumptions is neither informally nor formally clear, and some symbols have not been correctly defined (see questions).




OTHER COMMENTS:
- "(..) novel approach designed to enhance LLM reasoning by integrating both inductive and deductive reasoning processes
within the prompt construction framework as the Figure 1 shows." What I understand from Figure 1 is that DID is increasing both the complexity and accuracy wrt IO and CoT methods. However, it is not explained nor what "complexity" refers to in here, nor in which dataset/task the metrics are measured. Hence I found the Figure quite confusing instead of useful.
-"Deductive reasoning, formalized by philosophers like Kant, involves (..)" -> please add a citation here.
-Observed dataset: I think it would me more general to have D_p=\{d_1,...,d_{n_p}\}, similar for the new data, as each problem can have a different number of data.
-"Based on Assumptions 3.1 and 3.1," typo.
- Why the paragraph "Limitations of Chain-of-Thought (CoT) under Assumptions" is in section 3.2? This aspect don't seem to be related to the DID definition. Also, how CoT differs from DID concretly? Is there a fixed alpha, or it relies on a totally different formulation?
- The definition of the complexity is incomplete. What are n_ind and n_ded?
- "The dynamic adjustment enabled by the DID framework, as necessitated by Assumptions 1 and 2, reduces error propagation (..)" Please explain elaborate more this sentence.
- I don't see how the "theoretical adaption analysis" is supported by the description of the framework in Section 3.2.

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confidence: 4
contribution: 3
initial_rating: 3
presentation: 2
questions: 1. How the hybrid objective function and dynamic adjustment is implemented? From my understanding, there's no "training" process in your setting. how error is calculated and how new instances are selected?
2. What're the prompts for inductive reasoning and deductive reasoning?
soundness: 2
strengths: 1. Adaptive reasoning is an important challenge for LLMs. The proposed approach is novel.
2. This paper selects three tasks ranging from various complexity, showing its improvement in flexibility and adaptability of LLMs in complex problem-solving tasks.
summary: This paper proposes a reasoning framework which dynamically integrates inductive reasoning and deductive reasoning. The proposed framework can adjust its strategy according to the evolving complexity of the problem. The effectiveness has been examined across a diverse set of complex tasks.
weaknesses: 1. Introduction is too long and does not say much.
2. Poor presentation
 - Figure 1 is ambiguous. how complexity is measured? And why models are arranged in x-axis (complexity)?
 - Figure 2 does not help understanding since the concept of "Evolved Hypotheses" in DID part is still too general. Need more information to demonstrate the overall framework. Illustrations of "Knowledge Base", "Extracted Patterns and Facts" seem unnecessary here. 
3. Need to improve the orgranization of methodology. Currently it mainly focuses on theoretical analysis, but lack of implementation details. A psuedo code of the algorithm might help readers to understand the overall pipeline.
4. Insufficient experiment baselines. The DID framework is an iterative approach, it's unfair to only compare with prompting method such as IO or CoT. Better to add iterative baselines such as ToT or GoT for a fair comparison.
5. Lack of insights in Discussion section. 5.2 and 5.3 are future works, and 5.1 is kind of speculations, without evidence and in-depth error analysis.

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confidence: 3
contribution: 2
initial_rating: 3
presentation: 3
questions: Please refer to the Weaknesses.
soundness: 2
strengths: The paper presents the Deductive and InDuctive (DID) method, which offers an approach to enhancing the reasoning capabilities of Large Language Models (LLMs) by integrating deductive and inductive reasoning within the prompt construction process. This method is inspired by cognitive science, aligning with how humans adapt their reasoning strategies.
summary: The paper introduces the Deductive and InDuctive (DID) method, an approach designed to enhance the reasoning capabilities of Large Language Models (LLMs) by dynamically integrating both deductive and inductive reasoning within the prompt construction process. The DID method is grounded in cognitive science models of human reasoning and aims to mirror human adaptive reasoning mechanisms. The paper empirically validates the efficacy of the DID method on AIW, MR-GSM8K, and Holiday Puzzle, demonstrating significant improvements in solution accuracy and reasoning quality without incurring substantial computational overhead.
weaknesses: - The insufficiency of the experimental validation is one of the paper's main limitations. The paper only provides empirical validation on three relatively simple datasets and lacks in-depth analysis. On one hand, the authors should consider validating their method on more realistic datasets to demonstrate the effectiveness and generalizability of the proposed approach. On the other hand, benchmarking the DID method against state-of-the-art methods on the same tasks would help position the DID method within the existing landscape of LLM reasoning techniques. This comparison is crucial for establishing the novelty and practical value of the DID framework in enhancing the reasoning capabilities of large language models.

- The paper could benefit from a more detailed comparison with existing methods, such as Tree of Thought (ToT) and Graph of Thought (GoT). It should clearly articulate how it differs and why these differences are significant. Providing a side-by-side comparison with a clear emphasis on the unique aspects of DID would strengthen the novelty argument.

- The paper mentions that the DID approach is inspired by cognitive science models of human reasoning. However, it could provide a deeper dive into the specific cognitive science theories it draws from and how DID reflects these theories. This would help readers understand the theoretical underpinnings better and assess the method's potential for aligning with human-like reasoning.

- The paper claims that the DID method achieves improvements without imposing substantial computational overhead. However, it would be beneficial to see a detailed analysis of the computational costs, including comparisons with other methods on the same level of computational cost (e.g., cot + self-consistent voting), to substantiate this claim.