LogicLLM-DPO Boosting Large Language Models with Symbolic Solvers for Faithful Logical Reasoning

LogicLLM-DPO

Project Authors: Maximiliano Galindo, Jesús Vázquez, Francisco López

The project is carried out with the support and collaboration of the GIL (Linguistic Engineering Group) of the National Autonomous University of Mexico.

Introduction

The original article presents a framework that enables large language models (LLMs) to perform logical reasoning tasks. The framework is based on the idea of using a symbolic solver to generate logical formulas that are subsequently used to guide the LLM in its reasoning process. The authors demonstrate that this approach can significantly improve the performance of LLMs in logical reasoning tasks.

Key Ideas:

The LLM generates a logic program from an instruction.
A symbolic solver generates a formula that represents the solution to the problem.
The LLM uses this formula to generate the correct answer.

To improve the accuracy and number of successful translations of the LLM, the original article implements a self-refinement process that allows the LLM to iteratively improve its logic programs and formulas.

Installation and use

LOGIC-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning

Authored by Liangming Pan, Alon Albalak, Xinyi Wang, and William Yang Wang from the University of California, Santa Barbara, their work introduces a novel framework called LOGIC-LM, which integrates large language models (LLMs) with symbolic solvers to improve logical reasoning capabilities. The proposed approach consists of three main stages:

Problem formulation: The LLM translates the natural language problem into a suitable symbolic representation.
Symbolic reasoning: A deterministic symbolic solver makes inferences based on the symbolic formulation.
Result interpretation: The solver output is interpreted to derive the correct answer.

Additionally, a self-refinement module is incorporated that uses error messages from the symbolic solver to iteratively improve the accuracy of the logical representation.

The effectiveness of LOGIC-LM was evaluated on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. Results demonstrated an average improvement of 39.2% compared to LLMs with standard prompting and an 18.4% increase compared to LLMs with the chain-of-thought prompting method. These findings suggest that combining LLMs with symbolic logic offers a promising avenue for more faithful logical reasoning.