SWiM – A Semantic Wiki for Mathematical Knowledge Management

Lange, Christoph

doi:10.1007/978-3-540-68234-9_68

Cited by 15 publications

(11 citation statements)

References 6 publications

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“…Initial submissions can be verified or marked as sketches to be fully formalised later. Other mathematical web applications, such as the semantic wiki SWiM [38] and the document reader panta rhei [45], are not integrated with proof assistants but work with a central repository of mathematical knowledge represented in OpenMath [50] and OMDoc [35].…”

Section: An Environment For Correctness and Understandingmentioning

confidence: 99%

Formal Proof: Reconciling Correctness and Understanding

Calude

Müller

2009

Lecture Notes in Computer Science

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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.

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Section: An Environment For Correctness and Understandingmentioning

confidence: 99%

Formal Proof: Reconciling Correctness and Understanding

Calude

Müller

2009

Lecture Notes in Computer Science

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“…The semantic Wiki SWiM [Lan08] integrates the central libraries JOMDoc and JOBAD to handle and adapt mathematical notations. In fact, the developer of SWiM, Christoph Lange, is strongly involved in the implementation of both components.…”

Section: Notation Case Studiesmentioning

confidence: 99%

“…Moreover, workflows have been developed that allow to generate either format [W3C03,Ope07] from various scientific editor: LaTeXML [Mil07] allows to generate the respective XML from L A T E X. Editors of several web-based (authoring and E-Learning) environments, such as Sentido [GP06], MathDox [CCK + 08], ActiveMath [MS04], ConneXions [HBK03], and SWiM [Lan08], produce MathML and OpenMath, respectively. In addition, several mathematical computation systems provide an import & export from and to the two standards.…”

Section: Introductionmentioning

confidence: 99%

Context-Aware Adaptation: A Case Study On Mathematical Notations

Müller

Kohlhase

2009

Information Systems Management

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In the last two decades, the World Wide Web has become the universal, and -for many users -main information source. Search engines can efficiently serve daily life information needs due to the enormous redundancy of relevant resources on the web. For educational -and even more so for scientific information needs, the web functions much less efficiently: Scientific publishing is built on a culture of unique reference publications, and moreover abounds with specialized structures, such as technical nomenclature, notational conventions, references, tables, or graphs. Moreover, many of these structures are peculiar to specialized communities determined by nationality, research group membership, or adherence to a special school of thought. To keep the much-lamented "digital divide" from becoming a "cultural divide", we have to make online material more accessible and adaptable to individual users.In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordinarily interlinked. Modern, content-based representation formats like OpenMath or content MathML allow us to capture, model, relate, and represent mathematical knowledge objects and thus make them context-aware and machine-adaptable to the respective user contexts. Building on previous work which can make mathematical notations adaptable we employ user modeling techniques to make them adaptive to relieve the reader of configuration tasks. We present a comprehensive framework for adaptive notation management and evaluate it on an implementation integrated in the e-learning platform panta rhei.

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“…Concretely, we have extended the semantic T E X system S T E X [Koh06a] by PhysML functionality. For more choice in invasive editors, we will extend the OMDoc wiki system [LK06] and the PowerPoint plugin for OMDoc [KK04] to PhysML.…”

Section: Reading Writing and Arithmetic With Physml Documentsmentioning

confidence: 99%

Capturing the Content of Physics: Systems, Observables, and Experiments

Hilf

Kohlhase

Stamerjohanns

2006

Lecture Notes in Computer Science

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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.

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SWiM – A Semantic Wiki for Mathematical Knowledge Management

Cited by 15 publications

References 6 publications

Formal Proof: Reconciling Correctness and Understanding

Formal Proof: Reconciling Correctness and Understanding

Context-Aware Adaptation: A Case Study On Mathematical Notations

Capturing the Content of Physics: Systems, Observables, and Experiments

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