We tend to follow Maskin 2 004, § 3, defining restricted versions of the more general objects in ... more We tend to follow Maskin 2 004, § 3, defining restricted versions of the more general objects in Milgrom 2 004. In particular, we consider sealed-bid auctions with independently and identically distributed private values–according to a commonly known distribution–for a single indivisible good. 1
Page 1. Jacobs University Bremen – School of Engineering and Science Ph. D. hesis submitted in pa... more Page 1. Jacobs University Bremen – School of Engineering and Science Ph. D. hesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science Semantic Web Collaboration on Semiformal Mathematical Knowledge Christoph Lange Submitted: DD. MM. Dissertation Committee: Prof. Dr. Michael Kohlhase, Jacobs University Bremen (supervisor) Prof. Dr. Peter Baumann, Jacobs University Bremen Prof. Dr.
This paper shows how an explicit representation of units and quantities can improve the experienc... more This paper shows how an explicit representation of units and quantities can improve the experience of semantically published documents, and provides a first authoring method in this respect. To exemplify the potential and practical advantages of encoding explicit semantics regarding units wrt user experience, we demonstrate a unit system preference service, which enables the user to choose the system of units for the displayed paper.
Abstract. In this contribution we present some work we have been doing in representing and provin... more Abstract. In this contribution we present some work we have been doing in representing and proving theorems from the area of economics, and mainly we present work we will do in a project in which we will apply mechanised theorem proving tools to a class of economic problems for which very few general tools currently exist.
Abstract: At this http URL, the OpenMath 2 and 3 Content Dictionaries are accessible via a semant... more Abstract: At this http URL, the OpenMath 2 and 3 Content Dictionaries are accessible via a semantic wiki interface, powered by the SWiM system. We shortly introduce the inner workings of the system, then describe how to use it, and conclude with first experiences gained from OpenMath society members working with the system and an outlook to further development plans.
We study the formalization of a collection of documents created for a Software Engineering projec... more We study the formalization of a collection of documents created for a Software Engineering project from an MKM perspective. We analyze how document and collection markup formats can cope with an open-ended, multi-dimensional space of primary and secondary classifications and relationships. We show that RDFa-based extensions of MKM formats, employing flexible “metadata” relationships referencing specific vocabularies for distinct dimensions, are well-suited to encode this and to put it into service.
This paper describes the design and implementation of mechanisms for light-weight inclusion of fo... more This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting.
Abstract. A huge amount of documents is created and changed in our everyday life, so that Version... more Abstract. A huge amount of documents is created and changed in our everyday life, so that Version Control Systems like Git or SVN are tightly integrated with documents workflows. On the other hand, XML has come of age as a basis for document formats, and even though XML as a textbased format is suitable for version control in principle, the fact that version control systems work on files makes the integration of fragment access techniques like XPath or XQuery difficult.
SWiM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge... more SWiM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge represented in the domain-specific structural semantic markup language OMDoc. It motivates users to contribute to collections of mathematical knowledge by instantly sharing the benefits of knowledge-powered services with them. SWiM is currently being used for authoring content dictionaries, ie collections of uniquely identified mathematical symbols, and prepared for managing a large-scale proof formalisation effort.
Abstract. Mathematics, a ubiquitous foundation of science, technology, and engineering, is curren... more Abstract. Mathematics, a ubiquitous foundation of science, technology, and engineering, is currently missing from the Web of Data. This position paper argues why the future internet applications would benefit from mathematical knowledge published as Linked Open Data and outlines how mathematical knowledge could be contributed to the Web of Data. Due to the predominance of semantic XML-based markup languages in mathematics–which has good reasons–, this can not exclusively be achieved with RDF.
Documents are an important interface for interactive access to mathematical services. We will foc... more Documents are an important interface for interactive access to mathematical services. We will focus on web documents here, as a lot of mathematical content is already available on the web, and as web document formats like XHTML+ MathML with JavaScript allow for easily programming interactivity, which is not possible in rather static document formats like PDF. Our vision of an (inter) active document assumes that a reader wants to do more than just reading a document.
Mathematics is a ubiquitous foundation of science, technology, and engineering. Specific areas of... more Mathematics is a ubiquitous foundation of science, technology, and engineering. Specific areas of mathematics, such as numeric and symbolic computation or logics, enjoy considerable software support. Working mathematicians have recently started to adopt Web 2.0 environments, such as blogs and wikis, but these systems lack machine support for knowledge organization and reuse, and they are disconnected from tools such as computer algebra systems or interactive proof assistants.
Semantic markup languages support the workflow of structuring, annotating or reorganizing knowled... more Semantic markup languages support the workflow of structuring, annotating or reorganizing knowledge items Particularly common in the domain of mathematics (cf. preceding talk) SWiM is a semantic wiki for mathematical knowledge management We want to evaluate whether it will really support scientific knowledge engineering projects
Abstract. We discuss a vision of the Semantic Web where ontologies, services, and devices can sea... more Abstract. We discuss a vision of the Semantic Web where ontologies, services, and devices can seamlessly interoperate across a multitude of protocols and languages. In particular, we discuss the importance of enabling interoperability for Semantic Web technologies in the knowledge representation layer, and give an overview of the Distributed Ontology Language DOL addressing this aspect, representing a first piece of a Rosetta Stone enabling overall interoperability.
Abstract. Two tools addressing different aspects of educational mathematical documents have been ... more Abstract. Two tools addressing different aspects of educational mathematical documents have been developed in our research group and presented to the JEM community on previous occasions: SWiM is a semantic wiki for collaborating on such documents, and JOBAD is a framework that allows for reading documents interactively. In this paper, we outline a vision of an integrated educational environment for interactive learning and collaboration.
Abstract We present an extension of the Heterogeneous Tool Set HETS that enables proof support fo... more Abstract We present an extension of the Heterogeneous Tool Set HETS that enables proof support for Common Logic. This is achieved via logic translations that relate Common Logic and some of its sublogics to already supported logics and automated theorem proving systems. We thus provide the first full theorem proving support for Common Logic, including the possibility of verifying meta-theoretical relationships between Common Logic theories.
We tend to follow Maskin 2 004, § 3, defining restricted versions of the more general objects in ... more We tend to follow Maskin 2 004, § 3, defining restricted versions of the more general objects in Milgrom 2 004. In particular, we consider sealed-bid auctions with independently and identically distributed private values–according to a commonly known distribution–for a single indivisible good. 1
Page 1. Jacobs University Bremen – School of Engineering and Science Ph. D. hesis submitted in pa... more Page 1. Jacobs University Bremen – School of Engineering and Science Ph. D. hesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science Semantic Web Collaboration on Semiformal Mathematical Knowledge Christoph Lange Submitted: DD. MM. Dissertation Committee: Prof. Dr. Michael Kohlhase, Jacobs University Bremen (supervisor) Prof. Dr. Peter Baumann, Jacobs University Bremen Prof. Dr.
This paper shows how an explicit representation of units and quantities can improve the experienc... more This paper shows how an explicit representation of units and quantities can improve the experience of semantically published documents, and provides a first authoring method in this respect. To exemplify the potential and practical advantages of encoding explicit semantics regarding units wrt user experience, we demonstrate a unit system preference service, which enables the user to choose the system of units for the displayed paper.
Abstract. In this contribution we present some work we have been doing in representing and provin... more Abstract. In this contribution we present some work we have been doing in representing and proving theorems from the area of economics, and mainly we present work we will do in a project in which we will apply mechanised theorem proving tools to a class of economic problems for which very few general tools currently exist.
Abstract: At this http URL, the OpenMath 2 and 3 Content Dictionaries are accessible via a semant... more Abstract: At this http URL, the OpenMath 2 and 3 Content Dictionaries are accessible via a semantic wiki interface, powered by the SWiM system. We shortly introduce the inner workings of the system, then describe how to use it, and conclude with first experiences gained from OpenMath society members working with the system and an outlook to further development plans.
We study the formalization of a collection of documents created for a Software Engineering projec... more We study the formalization of a collection of documents created for a Software Engineering project from an MKM perspective. We analyze how document and collection markup formats can cope with an open-ended, multi-dimensional space of primary and secondary classifications and relationships. We show that RDFa-based extensions of MKM formats, employing flexible “metadata” relationships referencing specific vocabularies for distinct dimensions, are well-suited to encode this and to put it into service.
This paper describes the design and implementation of mechanisms for light-weight inclusion of fo... more This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting.
Abstract. A huge amount of documents is created and changed in our everyday life, so that Version... more Abstract. A huge amount of documents is created and changed in our everyday life, so that Version Control Systems like Git or SVN are tightly integrated with documents workflows. On the other hand, XML has come of age as a basis for document formats, and even though XML as a textbased format is suitable for version control in principle, the fact that version control systems work on files makes the integration of fragment access techniques like XPath or XQuery difficult.
SWiM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge... more SWiM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge represented in the domain-specific structural semantic markup language OMDoc. It motivates users to contribute to collections of mathematical knowledge by instantly sharing the benefits of knowledge-powered services with them. SWiM is currently being used for authoring content dictionaries, ie collections of uniquely identified mathematical symbols, and prepared for managing a large-scale proof formalisation effort.
Abstract. Mathematics, a ubiquitous foundation of science, technology, and engineering, is curren... more Abstract. Mathematics, a ubiquitous foundation of science, technology, and engineering, is currently missing from the Web of Data. This position paper argues why the future internet applications would benefit from mathematical knowledge published as Linked Open Data and outlines how mathematical knowledge could be contributed to the Web of Data. Due to the predominance of semantic XML-based markup languages in mathematics–which has good reasons–, this can not exclusively be achieved with RDF.
Documents are an important interface for interactive access to mathematical services. We will foc... more Documents are an important interface for interactive access to mathematical services. We will focus on web documents here, as a lot of mathematical content is already available on the web, and as web document formats like XHTML+ MathML with JavaScript allow for easily programming interactivity, which is not possible in rather static document formats like PDF. Our vision of an (inter) active document assumes that a reader wants to do more than just reading a document.
Mathematics is a ubiquitous foundation of science, technology, and engineering. Specific areas of... more Mathematics is a ubiquitous foundation of science, technology, and engineering. Specific areas of mathematics, such as numeric and symbolic computation or logics, enjoy considerable software support. Working mathematicians have recently started to adopt Web 2.0 environments, such as blogs and wikis, but these systems lack machine support for knowledge organization and reuse, and they are disconnected from tools such as computer algebra systems or interactive proof assistants.
Semantic markup languages support the workflow of structuring, annotating or reorganizing knowled... more Semantic markup languages support the workflow of structuring, annotating or reorganizing knowledge items Particularly common in the domain of mathematics (cf. preceding talk) SWiM is a semantic wiki for mathematical knowledge management We want to evaluate whether it will really support scientific knowledge engineering projects
Abstract. We discuss a vision of the Semantic Web where ontologies, services, and devices can sea... more Abstract. We discuss a vision of the Semantic Web where ontologies, services, and devices can seamlessly interoperate across a multitude of protocols and languages. In particular, we discuss the importance of enabling interoperability for Semantic Web technologies in the knowledge representation layer, and give an overview of the Distributed Ontology Language DOL addressing this aspect, representing a first piece of a Rosetta Stone enabling overall interoperability.
Abstract. Two tools addressing different aspects of educational mathematical documents have been ... more Abstract. Two tools addressing different aspects of educational mathematical documents have been developed in our research group and presented to the JEM community on previous occasions: SWiM is a semantic wiki for collaborating on such documents, and JOBAD is a framework that allows for reading documents interactively. In this paper, we outline a vision of an integrated educational environment for interactive learning and collaboration.
Abstract We present an extension of the Heterogeneous Tool Set HETS that enables proof support fo... more Abstract We present an extension of the Heterogeneous Tool Set HETS that enables proof support for Common Logic. This is achieved via logic translations that relate Common Logic and some of its sublogics to already supported logics and automated theorem proving systems. We thus provide the first full theorem proving support for Common Logic, including the possibility of verifying meta-theoretical relationships between Common Logic theories.
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