Proof of Thought : Neurosymbolic Program Synthesis allows Robust and Interpretable Reasoning (2409.17270v2)

Abstract: LLMs have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework that enhances the reliability and transparency of LLM outputs. Our approach bridges LLM-generated ideas with formal logic verification, employing a custom interpreter to convert LLM outputs into First Order Logic constructs for theorem prover scrutiny. Central to our method is an intermediary JSON-based Domain-Specific Language, which by design balances precise logical structures with intuitive human concepts. This hybrid representation enables both rigorous validation and accessible human comprehension of LLM reasoning processes. Key contributions include a robust type system with sort management for enhanced logical integrity, explicit representation of rules for clear distinction between factual and inferential knowledge, and a flexible architecture that allows for easy extension to various domain-specific applications. We demonstrate Proof of Thought's effectiveness through benchmarking on StrategyQA and a novel multimodal reasoning task, showing improved performance in open-ended scenarios. By providing verifiable and interpretable results, our technique addresses critical needs for AI system accountability and sets a foundation for human-in-the-loop oversight in high-stakes domains.

• The paper introduces the Proof of Thought framework to enhance LLM reasoning by combining neural outputs with formal logic verification.
• It employs a custom DSL and a robust type system to translate natural language into verifiable First Order Logic expressions using a theorem prover.
• Empirical results on StrategyQA and Reddit-OSHA demonstrate significant gains in accuracy and error reduction, reinforcing the framework's impact on AI trustworthiness.

Proof of Thought: Neurosymbolic Program Synthesis for Robust and Interpretable Reasoning

The paper at hand introduces a novel framework titled Proof of Thought (PoT), aiming to enhance the reliability and interpretability of LLMs when handling complex reasoning tasks. This framework synergizes LLM-generated outputs with formal logic verification mechanisms, promising a substantial improvement in AI accountability and trustworthiness.

Core Contributions

The PoT framework is articulated around several key contributions:

1. Logical Representation Generator: This component translates LLM-generated thoughts into formal logical expressions using a custom interpreter. The interpreter converts these representations into First Order Logic (FOL) constructs, which are then validated by a Z3 theorem prover.
2. Domain-Specific Language (DSL): An intermediate JSON-based DSL is introduced within PoT to balance rigorous logical structures and human-intuitive concepts. This hybrid representation facilitates both formal verification and accessible comprehension of LLM reasoning.
3. Robust Type System and Sort Management: PoT employs a strong type system with comprehensive sort management to ensure logical integrity across different reasoning domains. It emphasizes type-safe operations and pre-processing optimizations for logical terms.
4. Benchmarking on StrategyQA and Reddit-OSHA: The PoT framework is empirically validated through benchmarking on the StrategyQA dataset—an implicit multi-hop reasoning task—and a multimodal task involving hazardous scenario identification from the r/OSHA subreddit. The performance improvements, as shown by increased accuracy and reduced compilation errors, underline the practical efficacy of PoT.

Technical Insights

Logical Representation and Interpreter Design

The interpreter plays a pivotal role in PoT by systematically managing the transition from natural language to logical expressions. The comprehensive type system supports a variety of sorts, including primitive, declared (user-defined), enumerated, and composite (constructed from type constructors). This rigorous typing ensures type-safe substitutions and guards against semantic errors early in the reasoning process.

The symbol table and scope management are crucial for maintaining consistency across variable definitions and quantifier scopes. Parsing includes handling atomic formulas and complex formulas with logical connectives and quantifiers, with particular emphasis on correct quantifier scoping and term substitution.

The interpreter's pre-processing phase applies basic inference and simplification rules, reducing expressions using logical identities and converting them into a standard form, optimizing them for subsequent theorem proving. This stage also involves early error detection, identifying potential contradictions or type mismatches.

DSL Design and Capabilities

The DSL within PoT is meticulously designed to balance precision and intuitiveness. It includes constructs for sorts, functions, constants, variables, knowledge base axioms, rules, verifications, optimization constraints, and actions. Each component serves a specific purpose:

• Sorts and Functions: Define the domain of discourse and its interrelationships.
• Constants and Variables: Provide concrete grounding and variable scoping for logical operations.
• Knowledge Base and Rules: Establish foundational truths and inferential logic for domain-specific reasoning.
• Verifications and Actions: State the properties to verify and actions (such as 'verify' and 'optimize') to perform.

Empirical Evaluation

StrategyQA Performance: On the StrategyQA dataset, PoT demonstrates substantial improvements with a final accuracy of 82.4% after integrating a 3-step feedback loop for error correction. This iterative mechanism significantly increases the completion and success rates of logical programs. The high recall rate of 91.40% paired with a detailed F1-score of 71.13% indicates adept handling of true positive cases. Future revisions should aim to refine precision, addressing a notable false positive rate.

Reddit-OSHA Benchmark: PoT's application to the Reddit-OSHA dataset showcases its utility in multimodal reasoning tasks. Post feedback loop integration, the compilation error rate dropped to 0%, and the win rate on compiled programs reached 81.55%. This indicates PoT’s robustness in translating and verifying complex rules in diverse visual contexts.

Theoretical and Practical Implications

The introduction of Proof of Thought sets a new standard for interpretable and accountable AI. By embedding formal logic verification within the natural language reasoning pipeline, PoT provides a framework that enhances trust in AI outputs, especially in high-stakes applications such as health and safety compliance.

Theoretically, PoT advances the integration of neuro-symbolic AI, bridging the gap between the flexibility of neural networks and the rigor of symbolic logic. The hybrid DSL allows for scalable, generalizable logical reasoning that is both verifiable and interpretable.

Practically, PoT's framework offers immediate benefits for domains requiring explainable AI. The ability to trace reasoning paths and validate each inference step provides a clear advantage in auditing and oversight scenarios, facilitating human-in-the-loop configurations.

Future Directions

The research opens several avenues for future work. One direction is the expansion of PoT to handle more complex logical structures and non-boolean responses. Integrating reinforcement learning or fine-tuned models could further enhance reasoning accuracy. Another promising area is the application of PoT to larger, more diverse datasets, testing its scalability and generalizability across various domains.

In conclusion, Proof of Thought marries the interpretability of formal logic with the adaptability of LLMs, contributing a valuable tool to the quest for more trustworthy and reliable AI systems. Its application and theoretical underpinnings provide a substantial step forward, highlighting the potential for further advancements in neuro-symbolic AI.