Related papers: The GF Mathematics Library
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
MathGloss is a project to create a knowledge graph (KG) for undergraduate mathematics from text, automatically, using modern natural language processing (NLP) tools and resources already available on the web. MathGloss is a linked database…
The idea of a World digital mathematics library (DML) has been around since the turn of the 21th century. We feel that it is time to make it a reality, starting in a modest way from successful bricks that have already been built, but with…
This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…
We present some of the experiments we have performed to best test our design for a library for MathScheme, the mechanized mathematics software system we are building. We wish for our library design to use and reflect, as much as possible,…
In this paper we present an ongoing research investigating the possibility and potential of integrating frame semantics, particularly FrameNet, in the Grammatical Framework (GF) application grammar development. An important component of GF…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
This paper reports on the development of a Web platform to host the Mizar Mathematical Library (MML). In recent years, the size of formalized mathematical libraries has been drastically increasing, and this has led to a growing demand for…
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…
Grammatic is a tool for grammar definition and manipulation aimed to improve modularity and reuse of grammars and related development artifacts. It is independent from parsing technology and any other details of target system…
In this paper, we present a new approach to the semantic enrichment of mathematical expression problem. Our approach is a combination of statistical machine translation and disambiguation which makes use of surrounding text of the…
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human.…
This paper presents a currently bilingual but potentially multilingual FrameNet-based grammar library implemented in Grammatical Framework. The contribution of this paper is two-fold. First, it offers a methodological approach to…
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…
The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the…
This report provides an (updated) overview of {\sl Grafalgo}, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in…
This report provides the mathematical details of the gsplat library, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al. It provides a self-contained reference for the computations involved in the…