Generalizable and Faithful Logic Reasoning over Natural Language via Resolution Refutation

Core Concepts

The core message of this article is to propose a novel reasoning framework, named Generalizable and Faithful Reasoner (GFaiR), which introduces the paradigm of resolution refutation to improve the completeness and faithfulness of logic reasoning over natural language.

Abstract

The article presents a novel reasoning framework called GFaiR that aims to address the limitations of previous transformer-based reasoning systems. The key insights are:

Previous LLMs-based reasoning systems suffer from theoretical incompleteness, which restricts their ability to handle complex reasoning problems. To address this, GFaiR introduces the paradigm of resolution refutation, which has the capability to solve all first-order logic reasoning problems.

GFaiR consists of five key modules: a converter, a pre-selector, a post-selector, a knowledge composer, and a verifier. The converter transforms the natural language theory and hypothesis into a format suitable for resolution. The pre-selector and post-selector select relevant theories for the knowledge composer to apply resolution. The verifier ensures the selected theories can form a valid theory pair for resolution, improving the faithfulness of the reasoning process.

Experimental results show that GFaiR outperforms previous methods on complex reasoning scenarios while maintaining performance on simple scenarios. GFaiR also demonstrates strong zero-shot generalization abilities and faithfulness to its reasoning process.

The article also evaluates GFaiR on the natural language satisfiability (NLSAT) task, which requires reasoning solely based on rules without any facts. GFaiR outperforms the baseline methods on this more challenging task, further demonstrating its capability in handling complex reasoning scenarios.

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Key Insights Distilled From

Towards Generalizable and Faithful Logic Reasoning over Natural Language via Resolution Refutation

by Zhouhao Sun,... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01677.pdf

Deeper Inquiries

How can the resolution refutation paradigm introduced in GFaiR be extended to handle more complex logical constructs beyond first-order logic, such as higher-order logic or modal logic

The resolution refutation paradigm introduced in GFaiR can be extended to handle more complex logical constructs beyond first-order logic by adapting the resolution process to accommodate the rules and structures of higher-order logic or modal logic.
For higher-order logic, the resolution refutation process would need to consider quantification over functions and predicates, as well as higher-order variables. This would involve extending the resolution rule to handle higher-order terms and predicates, allowing for the resolution of statements involving functions and higher-order quantifiers.
In the case of modal logic, the resolution refutation process would need to incorporate modal operators such as necessity and possibility. This would require modifying the resolution rule to account for the semantics of modal logic, enabling the resolution of statements that involve modal operators and modal quantifiers.
By adapting the resolution refutation process to these more complex logical constructs, GFaiR could be enhanced to tackle a broader range of logical reasoning tasks that go beyond first-order logic.

What are the potential limitations of the validity contrastive loss-based verifier in GFaiR, and how could it be further improved to ensure the faithfulness of the reasoning process

The validity contrastive loss-based verifier in GFaiR may have potential limitations in scenarios where the logical relationships between theories are intricate or involve subtle nuances. In such cases, the verifier may struggle to accurately determine the validity of theory pairs, leading to potential errors in the reasoning process.
To improve the verifier and ensure the faithfulness of the reasoning process, several enhancements could be considered:

Enhanced Training Data: Providing the verifier with a more diverse and comprehensive set of training data that covers a wide range of complex logical relationships could improve its ability to distinguish valid conditions from illogical statements.
Fine-tuning and Calibration: Fine-tuning the verifier on a larger dataset and calibrating its parameters to better capture the nuances of logical reasoning could enhance its performance.
Incorporating Contextual Information: Integrating contextual information or prior knowledge into the verifier to help guide its decision-making process based on the broader context of the reasoning task.

By addressing these potential limitations and implementing these improvements, the validity contrastive loss-based verifier in GFaiR could be further refined to ensure the faithfulness and accuracy of the reasoning process.

Given the strong performance of GFaiR on the natural language satisfiability (NLSAT) task, how could the insights from this work be applied to other reasoning tasks that rely solely on rules, such as mathematical problem-solving or program synthesis

The insights gained from the strong performance of GFaiR on the natural language satisfiability (NLSAT) task can be applied to other reasoning tasks that rely solely on rules, such as mathematical problem-solving or program synthesis, in the following ways:

Rule-Based Reasoning: GFaiR's approach to reasoning based on rules and logical constructs can be leveraged in mathematical problem-solving tasks that involve following a set of rules or axioms to derive solutions. By adapting GFaiR's framework to mathematical domains, it can assist in automating the process of logical deduction and theorem proving in mathematics.

Program Synthesis: In program synthesis tasks, where the goal is to automatically generate programs based on a set of rules or specifications, GFaiR's methodology can be applied to reason about program correctness, constraints, and logical consistency. By utilizing GFaiR's reasoning capabilities, it can aid in the automated generation of programs that adhere to specified rules and requirements.

Knowledge Representation: GFaiR's ability to reason over formal logical theories expressed in natural language can be extended to knowledge representation tasks, where structured information needs to be interpreted and reasoned about. By applying GFaiR's approach to knowledge graphs or ontologies, it can facilitate more robust and accurate reasoning over complex knowledge structures.

By transferring the insights and methodologies from GFaiR to these related reasoning tasks, it is possible to enhance the efficiency, accuracy, and interpretability of automated reasoning systems in various domains.