Related papers: Maintaining a Library of Formal Mathematics
We introduce Merlion, an open-source machine learning library for time series. It features a unified interface for many commonly used models and datasets for anomaly detection and forecasting on both univariate and multivariate time series,…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…
MADlib is a free, open source library of in-database analytic methods. It provides an evolving suite of SQL-based algorithms for machine learning, data mining and statistics that run at scale within a database engine, with no need for data…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
To ensure the fairness and trustworthiness of machine learning (ML) systems, recent legislative initiatives and relevant research in the ML community have pointed out the need to document the data used to train ML models. Besides,…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately,…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
In today's world, we need to ensure that AI systems are fair and unbiased. Our study looked at tools designed to test the fairness of software to see if they are practical and easy for software developers to use. We found that while some…
Environments for systematic construction of logic programs are needed in the academy as well as in the industry. Such environments should support well defined construction methods and should be able to be extended and interact with other…
Most of the scientific software is developed in the same manner: It starts at a lab and the scientist says "This part of software is only for my private use". But the software grows and grows, and it comes the time, that other scientists…
Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics…
We introduce a machine-learning-based tool for the Lean proof assistant that suggests relevant premises for theorems being proved by a user. The design principles for the tool are (1) tight integration with the proof assistant, (2) ease of…
In this paper we present a new "external checker" for the Lean theorem prover, written in Lean itself. This is the first complete typechecker for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new checker…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
Machine learning (ML) in medicine has transitioned from research to concrete applications aimed at supporting several medical purposes like therapy selection, monitoring and treatment. Acceptance and effective adoption by clinicians and…
This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer…