Wolfram Sperber

Bringing mathematics to the web of data: the case of the mathematics subject classification

The Mathematics Subject Classification (MSC), maintained by the American Mathematical Societys Mathematical Reviews (MR) and FIZ Karlsruhes Zentralblatt fur Mathematik (Zbl), is a scheme for classifying publications in mathematics. While it is widely used, its traditional, idiosyncratic conceptualization and representation did not encourage wide reuse on the Web, and it made the scheme hard to maintain. We have reimplemented its current version MSC2010 as a Linked Open Dataset using SKOS, and our focus is concentrated on turning it into the new MSC authority. This paper explains the motivation and details of our design considerations and how we realized them in the implementation, presents use cases, and future applications.

Archiving Software Surrogates on the Web for Future Reference

Software has long been established as an essential aspect of the scientific process in mathematics and other disciplines. However, reliably referencing software in scientific publications is still challenging for various reasons. A crucial factor is that software dynamics with temporal versions or states are difficult to capture over time. We propose to archive and reference surrogates instead, which can be found on the Web and reflect the actual software to a remarkable extent. Our study shows that about a half of the webpages of software are already archived with almost all of them including some kind of documentation.

POS Tagging and Its Applications for Mathematics

Content analysis of scientific publications is a nontrivial task, but a useful and important one for scientific information services. In the Gutenberg era it was a domain of human experts; in the digital age many machine-based methods, e.g., graph analysis tools and machine-learning techniques, have been developed for it. Natural Language Processing (NLP) is a powerful machine-learning approach to semiautomatic speech and language processing, which is also applicable to mathematics. The well established methods of NLP have to be adjusted for the special needs of mathematics, in particular for handling mathematical formulae. We demonstrate a mathematics-aware part of speech tagger and give a short overview about our adaptation of NLP methods for mathematical publications. We show the use of the tools developed for key phrase extraction and classification in the database zbMATH.

swMATH: a new information service for mathematical software

An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information about it. The approach and the state of the art of the information service are described here.

Reimplementing the mathematics subject classification (MSC) as a linked open dataset

The Mathematics Subject Classification (MSC) is a widely used scheme for classifying documents in mathematics by subject. Its traditional, idiosyncratic conceptualization and representation makes the scheme hard to maintain and requires custom implementations of search, query and annotation support. This limits uptake e.g. in semantic web technologies in general and the creation and exploration of connections between mathematics and related domains (e.g. science) in particular. This paper presents the new official implementation of the MSC2010 as a Linked Open Dataset, building on SKOS (Simple Knowledge Organization System). We provide a brief overview of the datasets structure, its available implementations, and first applications.

Intelligent Computer Mathematics

This paper presents a proof language based on the work of Sacerdoti Coen (1,2), Kirchner (3) and Autexier (4) on ¯˜, a calculus introduced by Curien and Herbelin (5,6). Just as ¯˜ preserves several proof structures that are identified by the λ-calculus, the proof language presented here aims to preserve as much proof structure as reasonable; we call that property being logically saturated. This leads to several ad- vantages when the language is used as a generic exchange language for proofs, as well as for other uses. We equip the calculus with a simple rendering in pseudo-natural lan- guage that aims to give people tools to read, understand and exchange terms of the language. We show how this rendering can, at the cost of some more complexity, be made to produce text that is more natural and idiomatic, or in the style of a declarative proof language like Isar or Mizar.

Design, concepts, and state of the art of the swMATH service

In this paper, the concepts and design for an efficient information service for mathematical software and further mathematical research data are presented. The publication-based approach and the web-based approach are the main building blocks of the service and will be discussed. Heuristic methods are used for identification, extraction, and ranking of information about software and other mathematical research data. The methods provide not only information about the research data but also link software and mathematical research data to the scientific context.

The SMGloM Project and System: Towards a Terminology and Ontology for Mathematics

Mathematical vernacular – the everyday language we use to communicate about mathematics is characterized by a special vocabulary. If we want to support humans with mathematical documents, we need to extract their semantics and for that we need a resource that captures the terminological, linguistic, and ontological aspects of the mathematical vocabulary. In the SMGloM project and system, we aim to do just this. We present the glossary system prototype, the content organization, and the envisioned community aspects.

Mathematical Research Data, Software, Models, and the Publication-Based Approach

Scientific publications are still the most important medium for publishing mathematical research results. They serve as a container for different types of mathematical research data, especially mathematical models, theories, theorems, conjectures, proofs, algorithms, etc. They also link to mathematical software and simulations which has became more and more important for mathematics and applications. Therefore it seems to be natural to use publications for a more sophisticated analysis of mathematical research data, especially software. Mathematical publications are well-structured and use a more or less standard terminology for content, e.g., theorems, proofs, etc, and the formal structure. Nevertheless, publications could be used as a starting point to develop information services for mathematical research data. In the talk, the publication-based approach for mathematical software and a possible extension to mathematical models are discussed.

Software Citations, Information Systems, and Beyond

Even though software plays an ever-increasing role in today’s research and engineering processes, the scholarly publication process has not quite caught up with this. In particular, referencing and citing software remains problematic. Citations for publications are well-standardized but don’t immediately apply to software as, for instance, (a) software information is extremely heterogeneous, (b) software code is not persistent, and (c) the level of software information is often too coarse-granular.