Abstract. We present a content markup language for physics realized by extending the OMDoc format by an infrastructure for the principal concepts of physics: observables, physical systems, and experiments. The formalization of the description of physics observables follows the structural essence of the operational theory of physics measurements. The representational infrastructure for systems and experiments allow to capture the distinctive practice of physics: natural laws are supported by evidence from experiments which are described, disseminated and reproduced by others. 1

Abstract. There are many styles for the narrative structure of a mathematical document. Each mathematician has its own conventions and traditions about labeling portions of texts (e.g., chapter, section, theorem or proof) and identifying statements according to their logical importance (e.g., theorem is more important than lemma). Such narrative/structuring labels guide the reader’s navigation of the text and form the key components in the reasoning structure of the theory reflected in the text. We present in this paper a method to computerise the narrative structure of a text which includes the relationships between labeled text entities. These labels and relations are input by the user on top of their natural language text. This narrative structure is then automatically analysed to check its consistency. This automatic analysis consists of two phases: (1) checking the correct usage of labels and relations (i.e., that a “proof” justifies a “theorem ” but cannot justify an “axiom”) and (2) checking that the logical precedences in the document are self-consistent. The development of this method was driven by the experience of computerising a number of mathematical documents (covering different authoring styles). We illustrate how such computerised narrative structure could be used for further manipulations, i.e. to build a skeleton of a formal document in a formal system like Mizar, Coq or Isabelle. 1

International University Bremen,

Abstract. On the Web 2.0, there are numerous projects for collaboratively creating and using scientific knowledge in a wiki—think of the scientific sections of Wikipedia or domain-specific platforms like PlanetMath. They do, however, not yet offer semantic services that could promote collaboration both of scientific knowledge engineers and of scholars or that take semantics emerged from such communities or acquired from page contents into account. On the other hand, there are several semantic wikis—wikis enhanced with Semantic Web technologies. Current semantic wikis, however, only offer rather generic semantic services, such as semantic navigation, semantic-based editing assistance, and semantic search. Semantic services tailored to scientific knowledge and its specific structures (e. g. theories depending upon each other) are not yet provided. Based on the argument that current semantic wikis lack scientific services because domain-specific ontologies are not properly integrated, this article

Abstract. Semantic wikis have been successfully applied to many problems in knowledge management and collaborative authoring. They are particularly appropriate for scientific and mathematical collaboration. In previous work we described an ontology for mathematical knowledge based on the semantic markup language OMDoc and a semantic wiki using both. We are now evaluating these technologies in concrete application scenarios. In this paper we evaluate the applicability of our infrastructure to mathematical knowledge management by focusing on the Flyspeck project, a formalization of Thomas Hales ’ proof of the Kepler Conjecture. After describing the Flyspeck project and its requirements in detail, we evaluate the applicability of two wiki prototypes to Flyspeck, one based on Semantic MediaWiki and another on our mathematics-specific semantic wiki SWiM. 1 Scientific Communication and the Flyspeck Project Scientific communication consists mainly of exchanging documents, and a great deal of scientific work consists of collaboratively authoring them. Common instances are writing down first hypotheses, commenting on results of experiments or project steps, and structuring, annotating, or re-organizing existing items of knowledge, as depicted in Buchberger’s figure on the right.

Today’s scientific research is mostly acquired and shared using internet resources. In this context web collaboration has become more important these days. The paper presents the semantic knowledge wiki KnowWE that is used to capture and share ontological knowledge together with explicit problem solving knowledge in an open web environment. We also sketch a scientific research project using KnowWE as a knowledge pool and we show that distributed knowledge formalization poses new research questions concerning the quality and refactoring of knowledge. 1

Abstract. We present semantic markup as a way to exploit the semantics of mathematics in a wiki. Semantic markup makes mathematical knowledge machine-processable and thus allows for a multitude of useful applications. But as it is hard to read and write for humans, an editor needs to understand its inherent semantics and allow for a humanreadable presentation. The semantic wiki SWiM offers this support for the OpenMath markup language. Using OpenMath as an example, we present a way of integrating a semantic markup language into a semantic wiki using a document ontology and extracting RDF triples from XML markup. As a benefit gained from making semantics explicit, we show how SWiM supports the collaborative editing of definitions of mathematical symbols and their visual appearance. 1 Making Mathematical Wikis More Semantic What does a wiki need in order to support mathematics in a semantic way? First, there needs to be a way to edit mathematical formulæ. Many wikis offer

Abstract. Mathematical documents, and their instrumentation by computers, have rich structure at the layers of presentation, metadata and semantics, as objects in a system for formal mathematical logic. Semantic Web tools [2] support the first two of these, with little, if any, contribution to the third, while Proof Assistants [17] instrument the third layer, typically with bespoke approaches to the first two. Our position is that a web of mathematical documents, definitions and proofs should be given a fully-fledged semantics in terms of the third layer. We propose a “Math-Wiki ” to harness Web 2.0 tools and techniques to the rich semantics furnished by contemporary Proof Assistants. 1 Background and state of the art We can identify four worlds of mathematical discourse available on the Web: – Traditional mathematical practice: a systematic body of knowledge, organised around documents written by experts, most often in L ATEX, to varying degrees of sophistication. The intended audience is an expert readership, and

A good proof is a proof that makes us wiser. Manin [41, p. 209]. Abstract. Hilbert’s concept of formal proof is an ideal of rigour for mathematics which has important applications in mathematical logic, but seems irrelevant for the practice of mathematics. The advent, in the last twenty years, of proof assistants was followed by an impressive record of deep mathematical theorems formally proved. Formal proof is practically achievable. With formal proof, correctness reaches a standard that no pen-and-paper proof can match, but an essential component of mathematics — the insight and understanding — seems to be in short supply. So, what makes a proof understandable? To answer this question we first suggest a list of symptoms of understanding. We then propose a vision of an environment in which users can write and check formal proofs as well as query them with reference to the symptoms of understanding. In this way, the environment reconciles the main features of proof: correctness and understanding. 1

Abstract. Wikis are prominent for successfully supporting the quick and simple creation, sharing and management of content on the web. Semantic wikis improve this by semantically enriched content. Currently, notable advances in different fields of semantic technology like (paraconsistent) reasoning, expressive knowledge (e.g., rules), and ontology learning can be observed. By making use of these technologies, semantic wikis should not only allow for the agile change of its content but also the fast and easy integration of emerging semantic technologies into the system. Following this idea, the paper introduces an extensible semantic wiki architecture. 1