Using Large Language Models for Automated Formalization and Natural Language Argumentation Exercises for Beginner Students

Core Concepts

The author describes two systems that use large language models to automate the correction of exercises in translating between natural language and formal logic, as well as exercises in writing simple arguments in natural language.

Abstract

The author discusses two systems being developed that use large language models (LLMs) for automated tasks in teaching logic and reasoning:

Autoformalization:

Autoformalization is the automated translation from natural language to formal logic.
The author experimented with using text-davinci-003 and GPT-4-Turbo for this task.
With text-davinci-003, the performance was satisfactory for simple examples, but the model had issues with strange or absurd content, using all available notation, and high logical complexity.
GPT-4-Turbo showed better performance, correctly formalizing around 96.5% of the sample sentences in propositional logic and 92% in first-order logic.
Local LLMs focused on code-writing, like WizardCoder-34B, also showed reasonable results for propositional logic, though not as good as GPT-4-Turbo.

Natural Language Argumentation Exercises:

These exercises involve practicing logical argumentation in non-mathematical contexts.
The natural language input can be automatically translated into propositional logic using the same LLM-based approach.
The formal representation can then be passed to the Diproche system, which provides feedback on the logical correctness of the argument.

The author notes that the systems are currently in an experimental stage, with challenges around pricing and stability of the underlying LLMs that need to be overcome before actual deployment in teaching.

Stats

"If the sun shines, Hans goes for a walk. When Hans goes for a walk, he takes his dog with him. When Hans takes his dog for a walk, the dog barks at the cat on the neighbour's roof. When the dog barks at the cat on the roof, the cat runs away. However, the cat still sits on the roof."
"Barking dogs don't bark"
"Barking cats don't bite"

Quotes

None

Key Insights Distilled From

Using Large Language Models for (De-)Formalization and Natural Argumentation Exercises for Beginner's Students

by Merlin Carl at arxiv.org 04-03-2024

https://arxiv.org/pdf/2304.06186.pdf

Deeper Inquiries

How could the systems be extended to handle more complex logical structures or mathematical content beyond the beginner level?

To handle more complex logical structures or mathematical content beyond the beginner level, the systems could be enhanced in several ways:

Advanced Training Data: Providing the systems with a more extensive and diverse set of training data that includes complex logical structures and mathematical concepts would help them learn to handle higher-level content.

Fine-Tuning Models: Fine-tuning the existing large language models with specialized datasets containing advanced mathematical and logical problems would improve their ability to process and generate solutions for complex scenarios.

Integration of Advanced Logic: Incorporating more sophisticated logical rules, quantifiers, and mathematical symbols into the systems' capabilities would enable them to tackle advanced topics in logic and mathematics.

Feedback Mechanisms: Implementing feedback mechanisms that guide users through more intricate problems and provide explanations for complex solutions would support learners in understanding and mastering advanced concepts.

Collaborative Learning Features: Introducing collaborative learning features where users can work together on complex problems and receive feedback from peers or instructors would facilitate engagement with challenging content.

What are the potential limitations or biases of using large language models for these educational tasks, and how could they be mitigated?

Potential limitations and biases of using large language models for educational tasks include:

Limited Context Understanding: Large language models may struggle with understanding the full context of educational content, leading to inaccuracies in responses. Mitigation involves providing more context-specific training data and refining the models' contextual understanding.

Biased Training Data: Biases present in the training data can result in biased outputs from the models. To mitigate this, diverse and inclusive training datasets should be used, and bias detection mechanisms should be implemented to identify and address biases in real-time.

Overreliance on Model Outputs: There is a risk of students becoming overly dependent on the model's responses without fully grasping the underlying concepts. To address this, educators should encourage critical thinking and provide supplementary explanations alongside model-generated answers.

Lack of Explanation: Large language models may not always provide transparent explanations for their outputs, hindering students' understanding. Implementing features that offer detailed explanations for the model's reasoning can help mitigate this limitation.

Ethical Concerns: Ethical considerations, such as data privacy and algorithmic transparency, need to be addressed to ensure the responsible use of large language models in education.

How could the natural language argumentation exercises be adapted or expanded to other domains beyond everyday scenarios, such as philosophical or ethical reasoning?

To adapt natural language argumentation exercises to domains beyond everyday scenarios like philosophical or ethical reasoning, the following strategies could be employed:

Specialized Vocabulary: Introduce domain-specific vocabulary and concepts relevant to philosophical or ethical reasoning to create exercises tailored to these areas.

Complex Argument Structures: Design exercises that involve intricate argument structures, logical reasoning, and critical thinking specific to philosophical or ethical debates.

Ethical Dilemmas: Present students with ethical dilemmas and prompt them to construct arguments using natural language to justify their positions, fostering ethical reasoning skills.

Philosophical Debates: Create exercises that simulate philosophical debates on topics like ethics, metaphysics, or epistemology, requiring students to articulate and defend their positions in natural language.

Feedback from Experts: Incorporate feedback from domain experts in philosophy or ethics to evaluate students' argumentation exercises and provide insights into improving their reasoning skills in these specialized domains.