TLDR: This research introduces a novel method to significantly improve Large Language Models’ (LLMs) logical reasoning by adaptively selecting the most appropriate symbolic language (First-Order Logic, Logic Programming, or Boolean Satisfiability) for each problem before translation. Experiments show this adaptive approach dramatically outperforms fixed or random language choices, achieving 96% accuracy on mixed datasets and highlighting that different logical problems require different symbolic formalizations for optimal performance.
Large Language Models (LLMs) have shown impressive capabilities across many natural language processing tasks, but they often struggle with complex logical reasoning. This limitation can hinder their application in real-world scenarios where precise and verifiable reasoning is crucial.
Current efforts to improve LLM logical reasoning generally fall into three categories: prompt-based methods, fine-tuning methods, and external solver-based methods. This research focuses on the latter, where natural language problems are translated into a symbolic language (SL) and then solved by specialized logical solvers. While external solvers offer reliable and verifiable reasoning, their performance is highly dependent on the accuracy of this initial translation.
The Overlooked Factor in Translation Accuracy
Previous work aimed at improving translation accuracy primarily focused on how well the meaning of the symbolic language aligned with the natural language problem. However, this paper highlights a critical, often overlooked factor: the selection of the target symbolic language itself. Different logical problems are inherently better suited for different symbolic formalisms. For example, First-Order Logic (FOL) excels at problems involving complex quantifiers and categorical syllogisms, while Boolean Satisfiability (SAT) is more effective for constraint satisfaction and ordering problems.
The researchers found that using an inappropriate symbolic language, even with high semantic similarity in translation, can lead to significantly lower reasoning accuracy. For instance, on the LogicalDeduction dataset, SAT achieved 90% accuracy, while FOL only managed 42%. Conversely, for the ProofWriter dataset, FOL reached 95.50% accuracy, whereas SAT dropped to 68.33%. This clearly demonstrates that a ‘one-size-fits-all’ approach to symbolic language translation is suboptimal.
Introducing Adaptive Symbolic Language Selection
To address this, the paper proposes a novel method that adaptively selects the most suitable symbolic language for each logical reasoning problem before translation. This approach leverages an LLM to make this crucial selection. The framework involves three main stages:
- Adaptive SL Selection: Given a natural language logical reasoning problem, an LLM is prompted to determine the most appropriate symbolic language among three candidates: First-Order Logic (FOL), Logic Programming (LP), and Boolean Satisfiability (SAT). The prompt provides the LLM with a comparative analysis of each language’s expressive features, advantages, and disadvantages.
- Translation: Once the optimal SL is chosen, the LLM translates the natural language problem into a syntactically correct and semantically faithful expression in the selected symbolic language.
- Reasoning: The generated symbolic expressions are then passed to their corresponding external logical solvers (Prover9 for FOL, Pyke for LP, and Z3 for SAT). These solvers perform the logical reasoning and return a definitive result, which is then converted back into the final answer (True, False, or Unknown).
The Three Symbolic Languages
The method utilizes three distinct symbolic languages:
- First-Order Logic (FOL): Ideal for problems with complex quantification and relationships between entities, such as mathematical theorems or categorical syllogisms.
- Logic Programming (LP): Best suited for deductive reasoning based on a set of facts and rules, effective for propositional logical reasoning.
- Boolean Satisfiability (SAT): Highly efficient for problems that can be reduced to boolean constraints, like arrangement puzzles, scheduling, or spatial reasoning.
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Remarkable Performance Improvements
Experiments conducted on benchmarks like ProntoQA, ProofWriter, and LogicalDeduction, as well as a mixed dataset, demonstrated the significant effectiveness of this adaptive selection method. The approach consistently outperformed baselines that either translated all problems into a single symbolic language or used random selection.
On the mixed dataset, the adaptive selection method achieved a remarkable 96.00% overall accuracy. This represents a substantial improvement of 25% compared to the second-highest accuracy achieved by a fixed First-Order Logic translation. This dramatic difference underscores the value of intelligently selecting the most suitable symbolic language for each problem instance.
This research marks a significant step forward in enhancing the logical reasoning capabilities of LLMs by recognizing and addressing the critical role of symbolic language selection. The paper can be found at Adaptive Selection of Symbolic Languages for Improving LLM Logical Reasoning.
