# Neuro-Symbolic Artificial Intelligence: Towards Improving the Reasoning Abilities of Large Language Models
**Authors**: Xiao-Wen Yang, Jie-Jing Shao, Lan-Zhe Guo, Bo-Wen Zhang, Zhi Zhou, Lin-Han Jia
## Abstract
Large Language Models (LLMs) have shown promising results across various tasks, yet their reasoning capabilities remain a fundamental challenge. Developing AI systems with strong reasoning capabilities is regarded as a crucial milestone in the pursuit of Artificial General Intelligence (AGI) and has garnered considerable attention from both academia and industry. Various techniques have been explored to enhance the reasoning capabilities of LLMs, with neuro-symbolic approaches being a particularly promising way. This paper comprehensively reviews recent developments in neuro-symbolic approaches for enhancing LLM reasoning. We first present a formalization of reasoning tasks and give a brief introduction to the neuro-symbolic learning paradigm. Then, we discuss neuro-symbolic methods for improving the reasoning capabilities of LLMs from three perspectives: Symbolic $\to$ LLM, LLM $\to$ Symbolic, and LLM $+$ Symbolic. Finally, we discuss several key challenges and promising future directions. We have also released a GitHub repository including papers and resources related to this survey: https://github.com/LAMDASZ-ML/Awesome-LLM-Reasoning-with-NeSy.
## 1 Introduction
The development of artificial intelligence (AI) has evolved through distinct phases, shaped by different paradigms. Symbolic AI, focused on manipulating symbols, logic, rules, and knowledge to mimic human problem-solving abilities, laid the foundation for AI research before the 1990s. However, it encountered significant challenges, particularly regarding scalability and flexibility to real-world applications with noisy raw sensory inputs. On the other hand, Connectionist AI, centered on neural networks and achieved remarkable success in data-driven machine learning. More recently, building on the success of transformer models, LLMs have demonstrated promising results in various tasks. However, many researchers have reported that LLMs struggle with complex reasoning problems; they only attempt to replicate reasoning steps in training data, and cannot really reason. More efforts must be devoted to overcoming these bottlenecks for developing strong reasoning models.
Building AI models with strong reasoning capabilities is a crucial milestone toward achieving AGI. To this end, numerous researchers have focused on enhancing the reasoning abilities of LLMs. Existing studies can be categorized into three categories based on the different stages of the reasoning model construction: Data Construction, including how to automatically generate/augment/annotate/select data with reasoning paths; Fine-Tuning, including supervised fine-tuning and reinforcement fine-tuning on reasoning specialized datasets, and Inference, including inference techniques ranging from CoT to test-time scaling. Various large reasoning models have also been released, including OpenAI O1, Qwen-QwQ, DeepSeek-R1, etc.
Among these explorations, Neuro-Symbolic (NeSy) methods demonstrate superior performance. NeSy aims to integrate the strengths of symbolic AI, which excels in complex reasoning, with neural networks, which are adept at learning from large datasets De Raedt et al. (2020). By integrating these approaches, we can build AI systems that not only learn from large datasets but also handle complex reasoning tasks in a human-like manner. NeSy AI aligns with the Dual Process Theory in cognitive science, which posits that human cognition consists of two systems: System 1, which is fast, intuitive, and unconscious (neural networks), and System 2, which is slower, more deliberate, and conscious, focusing on logical reasoning and problem-solving (symbolic reasoning). Therefore, NeSy is naturally a promising way to improve the reasoning abilities of LLMs.
In this paper, we aim to give a brief introduction on how to exploit NeSy methods to improve LLM reasoning. We first give a formulation of reasoning tasks in LLMs (§ 2). Next, we give an introduction about the basic NeSy paradigm (§ 3). Then, we discuss how NeSy methods could improve the reasoning abilities of LLMs from three perspectives, Symbolic $\to$ LLM, LLM $\to$ Symbolic, LLM $+$ Symbolic (§ 4). Finally, by examining these advancements, we discuss open challenges in this field and outline potential future work (§ 7).
## 2 What is Reasoning?
The general reasoning task can be characterized as a recursive process in which each step builds upon the preceding reasoning steps. Formally, the task is defined as follows: given an input problem $Q$ and background knowledge $K$ , the goal is to get the answer $A$ , satisfying $A=f(Q,K)$ , where $f$ denotes the function mapping the problem and background knowledge to the answer. The $Q$ and $K$ can be represented in different forms, such as natural language or symbolic. For the reasoning tasks, we also have a reasoning path $Z$ consists of a sequence of intermediate reasoning steps, $Z=\{z_{1},z_{2},\ldots,z_{n}\}$ , where $z_{i}$ represents the $i$ -th step and satisfies $z_{i}=g_{i}(Q,K,z_{1},z_{2},...,z_{i-1})$ . Here, $g_{i}$ is a reasoning function of the $i$ -th step that incorporates the input problem, the background knowledge, and the previous steps. The final answer $A$ corresponds to the result of the last step in the reasoning path, i.e., $A=z_{n}$ .
The reasoning function $g(\cdot)$ plays a central role across various reasoning scenarios, determining how new reasoning steps or conclusions are generated based on background knowledge and prior reasoning steps. The specific interpretations of the reasoning function $g(\cdot)$ vary across three primary reasoning types: deductive reasoning, inductive reasoning, and abductive reasoning.
- Deductive Reasoning: In deductive reasoning, the reasoning function $g(\cdot)$ applies rules in the knowledge base $K$ to the intermediate steps to generate new reasoning steps or conclusions. Formally,
$$
z_{i}=\texttt{ApplyLogicRules}(Q,K,z_{1},z_{2},...,z_{i-1})
$$
where $\texttt{ApplyLogicRules}(\cdot)$ is an operation based on formal logic.
- Inductive Reasoning: Inductive reasoning involves generalizing patterns or rules from specific examples. The reasoning function $g(\cdot)$ extracts broader patterns from the intermediate steps. Formally,
$$
z_{i}=\texttt{InducePattern}(Q,K,z_{1},z_{2},...,z_{i-1})
$$
where $\texttt{InducePattern}(\cdot)$ is a pattern-discovery function, often relying on statistics, machine learning, or human expertise.
- Abductive Reasoning: Abductive reasoning generates hypotheses to explain observed phenomena. The reasoning function $g(\cdot)$ identifies the most possible hypothesis for the previous reasoning steps. Formally,
$$
z_{i}=\texttt{GenerateHypothesis}(Q,K,z_{1},z_{2},...,z_{i-1})
$$
where $\texttt{GenerateHypothesis}(\cdot)$ is a hypothesis generation function that seeks to identify the most plausible hypothesis to explain $z_{i-1}$ .
## 3 What is Neuro-Symbolic AI?
Neuro-symbolic AI seeks to combine the learning capabilities of neural networks with the reasoning power of symbolic AI. This integration enables the development of AI systems that can learn from extensive datasets while applying knowledge, rules, and logical reasoning, allowing them to tackle tasks that require both intuitive and deliberate thinking. Specifically, we categorize neuro-symbolic AI into three types: Neuro helps Symbolic, Symbolic helps Neuro, and Hybrid Neuro-Symbolic Architecture. For a more fine-grained categorization, please refer to Henry A. Kautz’s lecture in AAAI 2020 Kautz (2022).
### 3.1 Neuro helps Symbolic
This branch predominantly relies on symbolic processing, yet incorporates neural networks to address limitations of symbolic systems. Pure symbolic AI faces some key limitations, e.g., 1) large search spaces that hinder efficient problem-solving; 2) dependence on precisely defined symbols, limiting the representation of abstract real-world concepts; and 3) a rigid, deterministic reasoning process that struggles with ambiguity and uncertainty. These challenges can be addressed by integrating neural components, leading to the proposal of various NeSy approaches.
Exploiting neural networks to accelerate reasoning in symbolic systems represents a classic technique, with a notable example being AlphaGo Silver et al. (2016). AlphaGo integrates neural networks into MCTS, employing reinforcement learning on large-scale datasets to train policy and value networks. This integration provides heuristic acceleration for symbolic search, significantly overcoming the limitation of the pure symbolic system.
To overcome the limitations of symbolic systems in grounding abstract symbolic concepts into sub-symbolic real-world representations, neural networks can be exploited to directly extract symbolic concepts from raw data. This is a well-established and enduring research area Taddeo and Floridi (2005). One recent representative work is NS-CL Mao et al. (2019), which uses a convolutional neural network to parse images and extract features, while symbolic reasoning modules interpret these features to answer complex questions about the images.
To address the limitations of symbolic systems in handling ambiguity and uncertain reasoning, various studies have focused on making the symbolic process differentiable. A prime example is $\partial$ ILP Evans and Grefenstette (2018), which introduces the differentiable properties of neural networks into inductive logic programming (ILP). These approaches preserve symbolic logical reasoning while leveraging neural networks to process uncertain and probabilistic information, enabling the recognition of complex patterns.
<details>
<summary>imgs/sym4LLM.png Details</summary>
### Visual Description
\n
## Diagram: Symbolic Generation & LLM Formalization
### Overview
The image presents a diagram illustrating two distinct approaches to problem-solving: "Symbolic Generation, LLM Imitation" and "LLM Formalize, Symbolic Augment". Both approaches involve a "Symbolic Engine" and a "Problem" component, but differ in how they interact and utilize a Large Language Model (LLM), represented by a set of colored circles. The diagram uses boxes, ovals, and arrows to depict the flow of information and processes.
### Components/Axes
The diagram is divided into two main sections, separated by a vertical dashed line. Each section contains the following components:
* **Symbolic Engine:** Represented by a green rectangle.
* **Problem:** Represented by a yellow oval.
* **LLM:** Represented by a cluster of colored circles (orange, blue, purple).
* **Output/Formalize/Informalize:** Text labels indicating the type of transformation.
* **Reasoning Path/Search Traces/Proof Process/Task Plans:** Text labels within a dashed box, representing different outputs from the Symbolic Engine.
* **Mutate:** Text label indicating a transformation process.
* **New Problem:** Represented by a yellow oval.
* **Boxes:** Representing intermediate states or results.
* **Arrows:** Indicating the direction of information flow.
### Detailed Analysis or Content Details
**Left Side: Symbolic Generation, LLM Imitation**
1. **Problem** (yellow oval) feeds into the **Symbolic Engine** (green rectangle).
2. The **Symbolic Engine** generates **Output** (text label).
3. The **Output** is further categorized into four components within a dashed box:
* **Reasoning Path**
* **Search Traces**
* **Proof Process**
* **Task Plans**
4. The **LLM** (orange, blue, purple circles) receives input from the **Symbolic Engine** and is used for **Fine Tuning**.
5. The **Fine Tuning** process feeds back into the **Problem** component.
**Right Side: LLM Formalize, Symbolic Augment**
1. A **Language Problem** (oval) is **Formalized** (text label) and sent to the **Symbolic Engine** (green rectangle). The Formalization step is linked to the LLM (orange, blue, purple circles).
2. The **Symbolic Engine** generates a series of boxes, representing intermediate states.
3. These boxes are then **Mutated** (text label).
4. The **Symbolic Engine** then **Informalizes** (text label) the mutated output, resulting in a **New Problem** (yellow oval).
**LLM Representation:** The LLM is consistently represented by a cluster of three circles: orange, blue, and purple. The order appears consistent across both sides of the diagram.
### Key Observations
* The diagram highlights a cyclical process in both approaches.
* The LLM plays different roles in each approach: imitation/fine-tuning versus formalization/augmentation.
* The left side focuses on generating outputs from symbolic reasoning, while the right side focuses on transforming problems using symbolic reasoning guided by LLM formalization.
* The diagram does not provide any quantitative data or numerical values. It is a conceptual illustration of processes.
### Interpretation
The diagram illustrates two contrasting strategies for integrating symbolic reasoning with Large Language Models. The "Symbolic Generation, LLM Imitation" approach uses the LLM to learn from the outputs of a symbolic engine, essentially mimicking its reasoning process through fine-tuning. This suggests a focus on improving the LLM's ability to *act* like a symbolic reasoner.
The "LLM Formalize, Symbolic Augment" approach leverages the LLM to translate natural language problems into a symbolic representation that can be processed by the symbolic engine. This suggests a focus on using the LLM to *enable* symbolic reasoning by providing a structured input. The subsequent mutation and informalization steps indicate a process of exploring the solution space and generating new problems.
The diagram implies that both approaches are iterative, with feedback loops that refine the problem or the LLM's behavior. The use of dashed lines and boxes suggests that certain processes are internal or represent intermediate states rather than concrete outputs. The diagram is a high-level conceptual overview and does not delve into the specific algorithms or techniques used in each approach.
</details>
Figure 1: Illustration of how symbolic methods can be exploited to provide reasoning data for LLMs.
### 3.2 Symbolic helps Neuro
This branch of studies predominantly relies on neural networks, yet incorporates symbolic components to facilitate specialized features, such as logical reasoning, or improve interpretability and trustworthiness. Predominantly, there are two main methodologies to achieve this integration.
The first way is symbolic regularization approaches, which treat symbolic knowledge and rules as optimization constraints in the learning objective to guide the training process of neural networks, ensuring that the model’s predictions align more closely with domain-specific knowledge. Representative methods include Semantic Loss Xu et al. (2018), which directly incorporates logical constraints into the training process as a penalization term, and Logic Tensor Networks (LTNs) Badreddine et al. (2022), which combine first-order logic with tensor-based computations, allowing neural networks to learn representations that satisfy logical rules.
The second way is model-based approaches, which try to modify the neural network by infusing symbolic knowledge into its structure directly, rather than externally guiding the training process of neural networks using constraints. This can be achieved by designing specific layers or modules that are informed by symbolic rules Marra et al. (2020). Compared with regularization techniques, model-based methods embed symbolic knowledge directly into the model’s structure and ensure the knowledge is always considered in both the training and inference stages.
### 3.3 Hybrid Neuro-Symbolic Architecture
Different from previous categories that are “symbolic-heavy” or “neural-heavy”, various studies seek to design new hybrid neuro-symbolic architecture to make symbolic and neural networks work simultaneously in a framework to better exploit their strengths.
DeepProbLog Manhaeve et al. (2019) and Abductive Learning (ABL) Zhou (2019) are two representative methods. DeepProbLog Manhaeve et al. (2019) integrates deep learning and probabilistic logic, focusing on the interaction between learning and reasoning. It extends probabilistic programming by introducing neural predicates, which act as a bridge between neural networks and symbolic reasoning. This allows the system to harness the strengths of both paradigms: the pattern recognition capabilities of deep learning and the structured reasoning of logic programming. By enabling end-to-end training, DeepProbLog demonstrates powerful abilities for tasks requiring both perception and logical inference. Abductive learning Zhou (2019) offers a framework that bridges machine learning and logical reasoning through inconsistency minimization, enabling the generation of pseudo-labels for intermediate symbolic concepts. Unlike DeepProbLog, ABL does not aim to make the symbolic system differentiable. Instead, it fully leverages the reasoning capabilities inherent in symbolic knowledge by employing abductive reasoning to sample pseudo-labels for intermediate symbols. Both methods are capable of concurrently updating neural networks and symbolic systems.
In this paper, we follow the above categorization and discuss neuro-symbolic AI for improving the reasoning abilities of LLMs in a similar categorization, i.e., Symbolic $\to$ LLM, LLM $\to$ Symbolic, and LLM $+$ Symbolic. Given the breadth of research in this area, we respectfully acknowledge that our discussion is limited to a subset of representative works that most effectively convey the key concepts.
## 4 Symbolic $\to$ LLM: Addressing the Reasoning Data Scarcity
Creating large-scale reasoning datasets with high-quality reasoning paths is essential for enhancing the reasoning capabilities of LLMs. However, constructing such datasets poses significant challenges, as ensuring logical rigor and coherence in step-by-step reasoning processes is inherently difficult. Moreover, data annotation, particularly step-wise annotation, is highly resource-intensive, further complicating the dataset development process. In contrast, symbolic methods are characterized by their rigorous reasoning abilities, offering a promising way to investigate how they might compensate for the lack of sufficient reasoning data.
In this section, we illustrate how to explore symbolic methods to help address the reasoning data scarcity problem. Specifically, we explore this direction from two perspectives, Symbolic Generation, LLM Imitation and LLM Formalize, Symbolic Augment. The main ideas of these paradigms are illustrated in Figure 1.
<details>
<summary>imgs/llm2sym.png Details</summary>
### Visual Description
\n
## Diagram: Three Approaches to Problem Solving
### Overview
The image presents a comparative diagram illustrating three distinct approaches to problem solving. The approaches are: **Do It**, **Solve It**, and **Prevent It**. The diagram uses a table format to compare these approaches across several key dimensions.
### Comparison Table
| Feature | Do It | Solve It | Prevent It |
|---|---|---|---|
| **Focus** | Immediate Action | Root Cause Analysis | Proactive Measures |
| **Problem State** | Problem Exists | Problem Exists | Potential Problem |
| **Timeframe** | Short-Term | Medium-Term | Long-Term |
| **Effort** | Low | Medium | High |
| **Cost** | Low | Medium | High |
| **Example** | Applying a bandage to a cut | Investigating why the cut happened and addressing the cause | Wearing gloves to prevent cuts |
| **Tools** | Quick Fixes, Band-Aids | 5 Whys, Fishbone Diagram | Risk Assessment, Process Improvement |
| **Outcome** | Temporary Relief | Corrective Action | Reduced Risk |
| **Sustainability** | Not Sustainable | Moderately Sustainable | Highly Sustainable |
### Detailed Explanation of Each Approach
#### 1. Do It
This approach focuses on taking immediate action to address a problem as it arises. It's a reactive strategy that prioritizes quick solutions. While it provides immediate relief, it doesn't address the underlying cause and is therefore not a sustainable solution.
#### 2. Solve It
The "Solve It" approach involves analyzing the root cause of the problem and implementing corrective actions to prevent it from recurring. This is a more proactive approach than "Do It" and aims for a more sustainable solution. Tools like the "5 Whys" and Fishbone diagrams are commonly used in this approach.
#### 3. Prevent It
This approach is the most proactive of the three. It focuses on identifying potential problems before they occur and implementing preventative measures to mitigate the risk. This requires a long-term perspective and a commitment to continuous improvement. Risk assessment and process improvement techniques are key to this approach.
### Conclusion
The diagram highlights the trade-offs between these three approaches. The best approach depends on the specific situation, considering factors such as the urgency of the problem, the available resources, and the desired level of sustainability.
</details>
Figure 2: Illustration of how LLMs integrate symbolic solvers, programs, tools, or search algorithms to facilitate the reasoning process.
### 4.1 Symbolic Generation, LLM Imitation
For problems that can be solved using symbolic methods, we can leverage these methods to generate logically rigorous reasoning paths. Fine-tuning LLMs on such datasets enables them to learn and potentially mimic the reasoning capabilities of symbolic methods. This idea is quite similar to knowledge distillation, but instead of distilling data from a stronger model, it distills data from symbolic methods. Representative symbolic methods that can be applied to generate reasoning data, including but not limited to logical reasoning algorithms, logic solvers, constraint optimization, search algorithms, etc.
Numerous efforts have been devoted to leveraging various symbolic methods for generating reasoning data and fine-tuning LLMs to be applied in different tasks. For example, AlphaGeometry Trinh et al. (2024) develops a symbolic deduction engine to obtain the reasoning solutions to geometry problems, and surpasses the performance of the average IMO contestant in proving Euclidean plane geometry theorems. LOGIPT Feng et al. (2024) proposes to generate logical reasoning processes via logical solvers and fine-tuning LLMs to mimic the reasoning process of logical solvers, enabling LLMs to acquire similar abilities for tackling deductive reasoning tasks. Procedure Cloning Yang et al. (2022), DualFormer Su et al. (2025), and SOS Gandhi et al. (2024) generate search traces with search algorithms, such as DFS, BFS, A ∗, MCTS, etc, and fine-tune LLMs to enable the model to learn to search and backtrack in the reasoning procedure. Planformer Pallagani et al. (2022) generates plans for classical planning tasks with the FastDownward planner and constructs a PDDL-based dataset to fine-tune LLMs for planning tasks. The goal of these methods is to internalize the abilities of the symbolic solvers into the LLMs by constructing datasets for fine-tuning the model, thereby enhancing the LLM’s reasoning abilities.
### 4.2 LLM Formalize, Symbolic Augment
Unlike previous studies that focus on generating reasoning data with symbolic methods and fine-tuning LLMs to mimic their capabilities, this line of research takes a different direction that aims to augment data with symbolic methods. The pipeline can typically be summarized as: firstly, we can transform informal natural language data into a formalized representation space; secondly, we employ symbolic rules or solvers to help augment the data in the formalized space; thirdly, we transform the symbolically represented data into natural language. The help of symbolic rules or solvers enables the automatic augmentation of reasoning data that is both linguistically diverse and logically rigorous, compared to data augmentation with LLMs solely.
There are also various studies in this direction. For example, NSDG Li et al. (2024) formalizes the language represented math problems into its symbolic version, represented by the SMT-LIB language, and mutates the symbolic problem to create new variants for the data augmentation. Then, the symbolic form is converted to the natural language version. LLMs act as a bridge between symbolic and natural language spaces in this process. AMR-DA Shou et al. (2022) converts the original language data into an abstract meaning representation graph (AMR), a structured semantic representation that encapsulates the logical structure of the sentence, upon which operations are performed to generate logically modified AMR graphs. The modified AMR graphs are subsequently converted back into text to create augmented data. Similar ideas have also been adopted in the legal reasoning Zhou et al. (2025), logical reasoning Qi et al. (2025), theorem proving Ünsal et al. (2024), etc. Such methods excel in ensuring the logical correctness of generated data through symbolic reasoning and unlocking the potential for unlimited data generation, as the complexity of symbolic spaces provides nearly infinite possibilities, greatly expanding the diversity and scale of available reasoning datasets.
## 5 LLM $\to$ Symbolic: Addressing the Reasoning Function Error
From the formulation of reasoning tasks, it can be observed that the reasoning function $g(\cdot)$ serves as the core component in the reasoning process. LLMs typically employ auto-regressive techniques to approximate this reasoning function. However, this approach inherently introduces errors. Even minor inaccuracies at each step can propagate and amplify over successive steps, eventually causing the reasoning outcomes to deviate substantially from the correct answers.
To address errors in reasoning functions, it is a promising way to replace the auto-regressive style reasoning function with external symbolic methods to enhance the rigor of intermediate reasoning steps. The underlying intuition is that LLMs are inherently less adept at precise, long-chain reasoning. Therefore, enabling them to learn how to invoke external modules provides a more effective approach to solving complex reasoning problems. Formally, for given indices $i$ and $j$ ( $j>i$ ), this type of method can be expressed as: $z_{j}=\texttt{ExternalModules}(z_{i})$ . Here, the reasoning steps are represented symbolically, serving as a prerequisite for applying such methods. The ExternalModules represents an external module that processes the input $z_{i}$ and produces the output $z_{j}$ directly. The commonly external modules include symbolic solvers, program interpreters, off-the-shelf models, APIs, tools, search algorithms, etc. The main ideas of these methods are illustrated in Figure 2.
### 5.1 Symbolic Solver Aided Methods
The core idea of symbolic solver aided methods is to utilize external symbolic solvers, such as logic programming, SMT solvers, theorem provers, PDDL planners, constraint optimization tools, etc, to replace multiple reasoning functions performed internally. The pipeline of these methods is straightforward: first, translate natural language problems into a formalized representation that symbolic solvers can process, then call the solver to derive the solution.
LogicLM Pan et al. (2023) and LINC Olausson et al. (2023) are some of the earlier attempts at this approach. These methods transform natural language problems into executable logical expressions and leverage logic solvers to obtain results. There is also a branch of studies that focuses on exploiting classical planning methods to deal with planning tasks such as classical planning or robotics. For example, LLM+P Liu et al. (2023) propose to incorporate a PPDL-based symbolic planner. It leverages the semantic understanding abilities of LLM to translate informal language into a formal PDDL language and then employs the Fast-Downward solver for the planning process.
An important research direction related to these methods is how to automatically translate natural language represented data into a formalized symbolic representation. This is also called AutoFormalization. Representative studies include autoformalization of first-order logic, mathematical statements, mathematical proofs, PDDL, symbolic world models, etc. Key challenges lie in how to improve the consistency and the efficiency of the autoformalization process.
### 5.2 Program-Aided Methods
Instead of exploiting symbolic solvers, there are also various studies that aim to exploit the program interpreter to help improve the accuracy of reasoning functions. The main pipeline is similar to symbolic solver aided methods, with the key difference being that these methods convert natural language into a programming language and leverage a program executor to derive the solution.
PAL (Program-Aided Language Model) Gao et al. (2023) and PoT (Program of Thought) Chen et al. (2023) are two representative program-aided methods. Specifically, they adopt LLMs to express the reasoning process as Python programming languages, and the computation is relegated to an external program executor. Except for the Python programs, Binder Cheng et al. (2023) converts the input problem to SQL and executes the program interpreter to obtain the answer. Instead of relying on the code interpreter solely, CoC (Chain of Code) Li et al. (2023) generates code or pseudo-code and then executes the code with a code interpreter if possible, and with an LMulator (language model emulating code) otherwise. Related methods have been successfully applied to mathematical reasoning, code generation, robotics, etc. These methods can be seen as augmenting the chain of thought with external program interpreters to enable more accurate and robust reasoning.
### 5.3 Tool-Aided Methods
Beyond symbolic solvers and program interpreters, numerous other tools, APIs, and off-the-shelf models that have been developed for various tasks can also be exploited to enhance the accuracy of reasoning functions. Examples include calculators for numerical computations, web search engines for common-sense reasoning, and pre-trained vision models for visual reasoning.
Different from symbolic solver or program aided methods, which translate the natural language problems into a formalized language, and call the symbolic solver or program executor to obtain the solution directly, tool-aided methods are more complex, since they typically require calling different tools in different reasoning steps. Therefore, the pipeline can be divided into four stages: task planning, tool selection, tool calling, response generation.
For example, in the visual reasoning tasks, VisProg Gupta and Kembhavi (2023) utilizes LLMs to generate a Python-like API call program, integrating various tools, such as image processing subroutines in OpenCV, and off-the-shelf vision models, to perform complex visual reasoning tasks based on natural language instructions. These ideas inspired various subsequent studies such as ViperGPT Surís et al. (2023), Chameleon Lu et al. (2024), VisualSkechpad Hu et al. (2024b), etc. For mathematical reasoning, Tora Gou et al. (2024) explores the integration of LLMs with the utilization of external tools such as computation libraries and symbolic solvers. The key differences among these methods lie in the choice of tool libraries tailored to specific tasks and the strategies used to equip LLMs with accurate tool-utilization capabilities. These strategies include prompt techniques and fine-tuning the model on a diverse set of collected tool-use trajectories, such as SFT or RLFT.
<details>
<summary>imgs/end2end.png Details</summary>
### Visual Description
\n
## Diagram: Symbolic Reasoning Framework
### Overview
The image depicts a diagram illustrating a symbolic reasoning framework composed of three interconnected modules: Symbolic Formatted Reasoning, Differentiable Symbolic Module, and Symbolic Feedback. The diagram uses circles and rectangles to represent components and arrows to indicate the flow of information between them. The overall structure suggests an iterative process where symbolic prompts are processed, refined through a differentiable module, and then evaluated with feedback.
### Components/Axes
The diagram is divided into three main sections, each representing a module. Each module contains circles labeled "Problem" and a series of connected circles with a "key" symbol. Rectangles represent "Answer" and "Symbolic Representation". The diagram also includes a legend at the bottom-left corner:
* Solid Black Border: Answer
* Dashed Black Border: Symbolic Representation
### Detailed Analysis or Content Details
**1. Symbolic Formatted Reasoning (Left Module):**
* Contains a circle labeled "Problem".
* An arrow points from "Symbolic Prompts" to the "Problem" circle, indicated by a "+" symbol.
* The "Problem" circle is connected to a series of four circles with a "key" symbol.
* An arrow points from these four circles to a set of four rectangles: two with solid black borders (representing "Answer") and two with dashed black borders (representing "Symbolic Representation").
**2. Differentiable Symbolic Module (Center Module):**
* Contains a circle labeled "Problem".
* An arrow points from the "Problem" circle to a series of four circles with a "key" symbol.
* An arrow points from these four circles to the "Differentiable Symbolic Module" component.
* An arrow points from the "Differentiable Symbolic Module" to a rectangle labeled "Answer".
**3. Symbolic Feedback (Right Module):**
* Contains a circle labeled "Problem".
* The "Problem" circle is connected to a series of four circles with a "key" symbol.
* An arrow points from these four circles to the "Symbolic Module".
* A dashed arrow points from the "Symbolic Module" back to the "Symbolic Module", labeled "Regularization/Reward".
### Key Observations
* The "Problem" circle appears in all three modules, suggesting it is a central element of the framework.
* The "key" symbol circles are consistently connected to the "Problem" circles, potentially representing intermediate steps or variables in the reasoning process.
* The "Symbolic Feedback" module introduces a feedback loop, indicating an iterative refinement process.
* The use of solid and dashed borders for rectangles distinguishes between "Answer" and "Symbolic Representation".
### Interpretation
The diagram illustrates a framework for symbolic reasoning that combines symbolic and differentiable approaches. The "Symbolic Formatted Reasoning" module likely represents the initial stage where symbolic prompts are used to define a problem. The "Differentiable Symbolic Module" then processes this problem using differentiable techniques, potentially for optimization or learning. Finally, the "Symbolic Feedback" module uses the results to refine the process through regularization or reward signals. The iterative nature of the framework, as indicated by the feedback loop, suggests a continuous improvement process. The diagram doesn't provide specific data or numerical values, but rather a conceptual overview of the framework's architecture and information flow. The consistent use of the "Problem" and "key" symbol circles across modules suggests a standardized representation of the reasoning process.
</details>
Figure 3: Illustration of the main ideas of end-to-end LLM+symbolic reasoning, including symbolic formatted reasoning, differential symbolic modules, and symbolic feedback.
### 5.4 Search Augmented Methods
The core process of traditional symbolic solvers, such as SMT solvers or PDDL planners, can be abstractly modeled as a search problem: finding solutions that satisfy given constraints within a potentially vast or even infinite solution space, and adopting various pruning strategies and optimization techniques to accelerate the search process. To achieve similar abilities to these symbolic methods, various methods aim to directly combine the search algorithms with the decoding procedure of LLMs to enhance the reasoning capabilities of LLMs. Formally, at the $i$ -th step of reasoning, $T$ reasoning functions are expanded, producing $T$ candidate reasoning results: $z_{i}^{(t)}=g_{i}^{(t)}(Q,K,z_{1},z_{2},\ldots,z_{i-1}),t=1,2,...,T$ , where $g_{i}^{(t)}$ represents the $t$ -th reasoning function, and this can be realized by using the sampling mechanism of a language model. Consequently, the reasoning process can be transformed into a search problem, allowing the incorporation of various search algorithms.
For example, DBS Zhu et al. (2024) proposes a decoding algorithm that integrates self-evaluation guidance via the beam search. SPaR Cheng et al. (2025) proposes a self-play framework integrating BFS and DFS to refine the response and improve the instruction-following abilities of LLMs. ChinaTravel Shao et al. (2024) exploits BFS and DFS to improve the travel planning abilities of LLMs. NeurologicA* Lu et al. (2022) incorporates heuristic estimates of future cost in the decoding process, like the A* search algorithms. Moreover, building on the advantages of MCTS in AlphaGo and AlphaZero, numerous studies have been devoted to exploring the integration of MCTS in the LLMs’ inference stage to extend reasoning chains and improve reasoning accuracy. The difference in this line of research mainly lies in the choice of search algorithms and their intended role, whether to guide more effective exploration in the reasoning process or to refine reward estimation through simulation. However, these methods have clear limitations, since more exploration leads to a huge computation cost in the inference time.
## 6 Symbolic $+$ LLMs: End-to-End Reasoning
In the previous two branches of research, LLMs and symbolic methods operate separately. For example, for the symbolic $\to$ LLMs paradigm, symbolic AI methods are responsible for generating or augmenting data, after which the LLMs are fine-tuned on these datasets. For LLMs $\to$ symbolic paradigm, the LLMs call symbolic solvers, which then derive the answer. A holy-grail problem for neuro-symbolic AI is designing mechanisms that enable symbolic methods and neural networks to work in a more hybrid or end-to-end fashion. Specifically, we review efforts about Symbolic $+$ LLMs in this direction from three perspectives, i.e., symbolic formatted reasoning, differential symbolic module, and symbolic feedback. The main ideas are illustrated in Figure 3.
### 6.1 Symbolic Formatted Reasoning
For the reasoning process in LLMs, the reasoning path $Z$ can be represented in various forms, such as natural language or latent embedding. In certain reasoning tasks, these representations may be prone to inaccuracies. Such representational errors can accumulate progressively as the reasoning chain lengthens, ultimately leading to significant deviations from the correct reasoning solutions.
To mitigate potential representation errors in reasoning chains, we may adopt formally symbolic representations to describe intermediate reasoning states, instead of relying solely on natural language descriptions or latent embedding. This symbolic representation offers significant advantages by providing more explicit and precise semantic expressions, thereby avoiding errors caused by the ambiguity of natural language or the vagueness of latent embedding. Formally, $\forall i\neq n,z_{i}\in\mathcal{L}$ , where $\mathcal{L}$ denotes a symbolic language defined over a predetermined alphabet. The final answer, $A$ , is derived from this sequence of intermediate symbolic representations.
Symbolic formatted reasoning is particularly suitable for tasks that can be precisely symbolized, such as mathematical reasoning. For example, NaturalPrompt Ling et al. (2023) enables LLMs to generate deductive reasoning chains using a proposed natural program format, Chain-of-Symbol prompting Hu et al. (2024a) prompts LLMs to convert natural language into concise symbolic representations, enhancing their performance on spatial tasks while significantly reducing token consumption. LogicGuide Poesia et al. (2024) introduces a general logical reasoning system to assist the LLM. It formalizes the reasoning process within LogicGuide, ensuring that step-by-step reasoning remains sound and reliable. There are also some methods that use programming languages like Python as the symbolic language for intermediate representations Weir et al. (2024). Unlike program-aided methods, the Python code is not executed but rather serves solely as a structured prompt to guide the model toward the final answer. These methods leverage symbolic representations to mitigate potential representation error accumulation inherent in natural language representations during the reasoning process. Alongside natural language and latent embedding representation reasoning, they form the three primary reasoning formations.
### 6.2 Differential Symbolic Module
Unlike machine learning, which relies on continuous numerical optimization, symbolic AI methods are typically grounded in discrete symbolic reduction. Consequently, designing a unified optimization framework that allows machine learning and symbolic reasoning to be jointly optimized remains a fundamental challenge. A promising direction is to develop differential symbolic modules to enable the symbolic reasoning systems to work with the machine learning models.
In classical NeSy studies, many efforts have been devoted to this direction. More recently, studies have emerged to develop differentiable symbolic modules that can seamlessly integrate with LLMs. For example, DiLA Zhang et al. (2024) leverages LLMs to parse natural language represented problem into a SAT problem which consists of a set of logical formulas, then LLM generates an initial solution based on its natural language understanding, next the relaxed variable and extracted constraints are offloaded to a differential logic layer, checking the constraint satisfiability, and updating the solution until all constraints are met. Oreoml Hu et al. (2022) propose to integrate knowledge graph reasoning of symbolic logic and neural networks, enabling the LLMs to work together with a differentiable knowledge graph reasoning module through the knowledge interaction layers embedded in the LLMs. NSVQA Amizadeh et al. (2020) leverages predicates as symbolic representations linked to neural modules that process visual elements, disentangle visual representation learning from the inference mechanism, and propose a differentiable first-order logic formalism based on fuzzy logic for compositional visual reasoning. AutoCoNN Weng et al. (2024) proposes a framework that synergistically integrates compiled neural networks (CoNNs) into the standard transformer architecture. CoNNs are neural modules designed to explicitly encode rules through artificially generated attention weights. By incorporating CoNN modules, the neural comprehension framework enables LLMs to execute rule-intensive symbolic tasks.
These methods represent initial attempts to enable joint optimization of logical reasoning and LLM fine-tuning. However, they still face significant challenges, such as open concepts, optimization efficiency, generality, etc. More efforts are needed to improve the efficiency, scalability, and robustness of these methods.
### 6.3 Symbolic Feedback
Supervised fine-tuning and reinforcement fine-tuning are two main learning paradigms for enhancing the reasoning capabilities of pre-trained LLMs. Both rely on supervisory signals, such as the supervised loss and the reward function, to guide the learning process. Symbolic methods offer more precise and interpretable verification capabilities. Therefore, exploring how to leverage them as regularization terms in the loss function for supervised fine-tuning or reward signals in reinforcement fine-tuning represents a promising and important research direction.
For supervised fine-tuning, Premsri and Kordjamshidi (2025) proposes to fine-tune LLMs by exploiting the spatial logical rules as constraints, providing additional supervision to improve spatial reasoning. For reinforcement fine-tuning, SyreLM Dutta et al. (2024) adopts a small frozen LM, equipped with an adapter, to translate natural language problems into formal language expressions, and adopts reinforcement learning to train the adapted LM, informed by the non-differentiable symbolic solver. RBR Mu et al. (2024) proposes rule-based rewards to improve the safety of LLMs. RLSF Jha et al. (2024) exploits various reasoning or domain knowledge tools (e.g., symbolic solvers, theorem provers, or knowledge bases) to provide feedback to the LLMs. Similar ideas have also been adopted by LLM-Modulo Kambhampati et al. (2024) for planning tasks, Cotran Jana et al. (2024) for code generation tasks, etc. This line of research is related to neuro-symbolic reinforcement learning. The advantages of these methods lie in that it does not require the symbolic methods to be differentiable.
## 7 Challenges & Open Research Directions
Despite the promising advances in NeSy approaches for enhancing reasoning capabilities in LLMs, several challenges persist. This section discusses key challenges and proposes open research directions to address them.
#### Multi-Modal Reasoning
Previous studies mainly focus on reasoning in language modality. Various real-world applications require multi-modal reasoning, such as VQA, embodied AI, spatial intelligence, etc. How to effectively exploit symbolic systems that are integrated with multi-modal language models remains an open problem. Moreover, existing multi-modal reasoning is mainly conducted on the language modalities. In contrast, human reasoning often involves the simultaneous processing of multiple modalities. For example, when solving geometry problems, humans may draw auxiliary lines on diagrams to support their reasoning. This highlights a significant gap between current approaches and human manner multi-modal reasoning.
#### Advanced Hybrid Architectures
Though LLMs achieve promising results across various tasks, they remain data-driven machine learning models that rely on statistical pattern recognition rather than formal logical reasoning. To construct AI systems with both abilities to exploit big data and perform rigorous reasoning, it is important to develop more advanced hybrid neuro-symbolic architectures that seamlessly integrate LLMs and symbolic reasoning components. More advanced optimization techniques are also required to improve the scalability and efficiency of these architectures.
#### Theoretical Understanding
The theoretical understanding of how symbolic methods enhance the reasoning abilities of LLMs is crucial for guiding the design of more effective algorithms. However, efforts towards this direction remain limited. For example, the generalization performance with symbolic methods, optimization theory for the LLMs fine-tuning with symbolic feedback, analysis on the reasoning shortcuts, the relationship between scaling laws and the integration of symbolic methods, etc. Further efforts are needed to establish solid theoretical foundations for LLMs’ reasoning.
## 8 Conclusion
Improving the reasoning capabilities of AI models is a key milestone towards AGI. This paper explores the role of neuro-symbolic methods in enhancing reasoning in LLMs. We give a formulation of reasoning tasks and introduce the main ideas from three perspectives, Symbolic $\to$ LLM, LLM $\to$ Symbolic, and LLM $+$ Symbolic, to explore how symbolic methods can be exploited to address critical challenges in LLMs’ reasoning, including reasoning data scarcity, reasoning function errors, representation errors, etc. Open challenges and opportunities are also discussed.
Given the rapid development of this field and the vast number of publications, it is not feasible to cover all papers comprehensively. Instead, we focus on presenting the key ideas and technical approaches. We aim for this paper to provide an up-to-date summary of recent advancements and inspire new insights into the integration of symbolic AI methods with LLMs for the development of strong reasoning models.
## Acknowledgments
This research was supported by National Science Foundation of China (62306133, 62206124), Key Program of Jiangsu Science Foundation (BK20243012), Jiangsu Science Foundation Leading-edge Technology Program (BK20232003) and Major Program (JD) of Hubei Province (2023BAA024).
## Contribution Statement
Equal contribution ( $*$ ): Xiao-Wen Yang, Jie-Jing Shao and Lan-Zhe Guo. Corresponding author( ${\dagger}$ ): Yu-Feng Li.
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