# SymBa: Symbolic Backward Chaining for Structured Natural Language Reasoning

arXiv: https://arxiv.org/abs/2402.12806 · HTML: https://mlsanity.com/paper/2402.12806/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 4 of 4)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Question Decomposition Improves the Faithfulness of Model-Generated Reasoning](https://mlsanity.com/paper/2307.11768/) (2023)
- [Computing Stable Models of Normal Logic Programs Without Grounding](https://mlsanity.com/paper/1709.00501/) (2017)

## Built on by (most cited first, 6 of 6)

- [Can Language Models Pretend Solvers? Logic Code Simulation with LLMs](https://mlsanity.com/paper/2403.16097/) (2024)
- [Goal-Oriented Reasoning for RAG-based Memory in Conversational Agentic LLM Systems](https://mlsanity.com/paper/2605.12213/) (2026)
- [Thinking Forward and Backward: Effective Backward Planning with Large Language Models](https://mlsanity.com/paper/2411.01790/) (2024)
- [From Hypothesis to Premises: LLM-based Backward Logical Reasoning with Selective Symbolic Translation](https://mlsanity.com/paper/2512.03360/) (2025)
- [A Balanced Neuro-Symbolic Approach for Commonsense Abductive Logic](https://mlsanity.com/paper/2601.18595/) (2026)
- [Revealing Algorithmic Deductive Circuits for Logical Reasoning](https://mlsanity.com/paper/2605.27824/) (2026)

## Abstract (arXiv)

To improve the performance and explainability of LLM-based natural language reasoning, structured reasoning can be applied to generate explicitly structured proofs. Among different methods for structured reasoning, we specifically focus on backward chaining, where the proof goal is recursively decomposed to subgoals by searching and applying rules. We argue that current LLM-based backward chaining systems (e.g. Least-to-most prompting and LAMBADA) are incomplete, as they omit crucial algorithmic components identified from the classic backward chaining algorithm in computational logic (SLD Resolution). To this end, we propose a novel backward chaining system, SymBa (Symbolic Backward Chaining), which integrates a symbolic solver and an LLM. In SymBa, the solver controls the proof process, and the LLM is only called when the solver requires new information to complete the proof. Empowered by completeness, SymBa achieves a significant improvement in seven deductive, relational, and arithmetic reasoning benchmarks compared to the baselines.