# Theorem-of-Thought: A Multi-Agent Framework for Abductive, Deductive, and Inductive Reasoning in Language Models

arXiv: https://arxiv.org/abs/2506.07106 · HTML: https://mlsanity.com/paper/2506.07106/

## 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 5 of its 26 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 5 of 5)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [SINdex: Semantic INconsistency Index for Hallucination Detection in LLMs](https://mlsanity.com/paper/2503.05980/) (2025)

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

- [From Language to Action: A Review of Large Language Models as Autonomous Agents and Tool Users](https://mlsanity.com/paper/2508.17281/) (2025)
- [Typed Chain-of-Thought: A Curry-Howard Framework for Verifying LLM Reasoning](https://mlsanity.com/paper/2510.01069/) (2025)
- [Think Locally, Explain Globally: Graph-Guided LLM Investigations via Local Reasoning and Belief Propagation](https://mlsanity.com/paper/2601.17915/) (2026)
- [GraphMind: Theorem Selection and Conclusion Generation Framework with Dynamic GNN for LLM Reasoning](https://mlsanity.com/paper/2511.19078/) (2025)
- [Knowledge Vector of Logical Reasoning in Large Language Models](https://mlsanity.com/paper/2604.23877/) (2026)
- [IsoSci: A Benchmark of Isomorphic Cross-Domain Science Problems for Evaluating Reasoning versus Knowledge Retrieval in LLMs](https://mlsanity.com/paper/2607.01431/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have shown strong performance across natural language reasoning tasks, yet their reasoning processes remain brittle and difficult to interpret. Prompting techniques like Chain-of-Thought (CoT) enhance reliability by eliciting intermediate reasoning steps or aggregating multiple outputs. However, they lack mechanisms for enforcing logical structure and assessing internal coherence. We introduce Theorem-of-Thought (ToTh), a novel framework that models reasoning as collaboration among three parallel agents, each simulating a distinct mode of inference: abductive, deductive, and inductive. Each agent produces a reasoning trace, which is structured into a formal reasoning graph. To evaluate consistency, we apply Bayesian belief propagation guided by natural language inference (NLI), assigning confidence scores to each step. The most coherent graph is selected to derive the final answer. Experiments on symbolic (WebOfLies) and numerical (MultiArith) reasoning benchmarks show that ToTh consistently outperforms CoT, Self-Consistency, and CoT-Decoding across multiple LLMs, while producing interpretable and logically grounded reasoning chains. Our findings suggest a promising direction for building more robust and cognitively inspired LLM reasoning. The implementation is available at https://github.com/KurbanIntelligenceLab/theorem-of-thought.