Related papers: Maintaining a Library of Formal Mathematics
The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple,…
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
This project investigated new approaches and technologies to enhance the accessibility of mathematical content and its semantic information for a broad range of information retrieval applications. To achieve this goal, the project addressed…
Software libraries are central to the functionality, security, and maintainability of modern code. As developers increasingly turn to Large Language Models (LLMs) to assist with programming tasks, understanding how these models recommend…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Just like the scientific data they generate, simulation workflows for research should be findable, accessible, interoperable, and reusable (FAIR). However, while significant progress has been made towards FAIR data, the majority of science…
The integration of retrieval-augmented techniques with LLMs has shown promise in improving performance across various domains. However, their utility in tasks requiring advanced reasoning, such as generating and evaluating mathematical…
In recent progress, mathematical verifiers have achieved success in mathematical reasoning tasks by validating the correctness of solutions generated by policy models. However, existing verifiers are trained with binary classification…
Building a repository of proof-checked mathematical knowledge is without any doubt a lot of work, and besides the actual formalization process there also is the task of maintaining the repository. Thus it seems obvious to keep a repsoitory…
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
Large Language Models (LLMs) are increasingly used for educational support, yet their response quality varies depending on the language of interaction. This paper presents an automated multilingual pipeline for generating, solving, and…
With the growing popularity of Large Reasoning Models and their results in solving mathematical problems, it becomes crucial to measure their capabilities. We introduce a pipeline for both automatic and interactive verification as a more…
Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…
We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions,…
A key challenge in developing and deploying Machine Learning (ML) systems is understanding their performance across a wide range of inputs. To address this challenge, we created the What-If Tool, an open-source application that allows…
Multi-Label Classification toolbox is a MATLAB/OCTAVE library for Multi-Label Classification (MLC). There exists a few Java libraries for MLC, but no MATLAB/OCTAVE library that covers various methods. This toolbox offers an environment for…
Creating fair AI systems is a complex problem that involves the assessment of context-dependent bias concerns. Existing research and programming libraries express specific concerns as measures of bias that they aim to constrain or mitigate.…
The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of compute-intensive applications now under development, particularly in science and…