Michael Kohlhase

Publications

• Licensing the Mizar Mathematical Library

  Jesse Alama, Michael Kohlhase, Adam Naumowicz, Piotr Rudnicki, Josef Urban, Lionel Mamane

  07/2011;

  The Mizar Mathematical Library (MML) is a large corpus of formalised mathematical knowledge. It has been constructed over the course of many years by a large number of authors and maintainers. Yet the legal status of these efforts of the Mizar community has never been clarified. In 2010, after many ... [more] The Mizar Mathematical Library (MML) is a large corpus of formalised mathematical knowledge. It has been constructed over the course of many years by a large number of authors and maintainers. Yet the legal status of these efforts of the Mizar community has never been clarified. In 2010, after many years of loose deliberations, the community decided to investigate the issue of licensing the content of the MML, thereby clarifying and crystallizing the status of the texts, the text's authors, and the library's long-term maintainers. The community has settled on a copyright and license policy that suits the peculiar features of Mizar and its community. In this paper we discuss the copyright and license solutions. We offer our experience in the hopes that the communities of other libraries of formalised mathematical knowledge might take up the legal and scientific problems that we addressed for Mizar.

• A Foundational View on Integration Problems

  Florian Rabe, Michael Kohlhase, Claudio Sacerdoti Coen

  05/2011;

  The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario ... [more] The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration.

• Workflows for the Management of Change in Science, Technologies, Engineering and Mathematics

  Serge Autexier, Catalin David, Dominik Dietrich, Michael Kohlhase, Vyacheslav Zholudev

  05/2011;

  Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately, machine support for change management has either been very ... [more] Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately, machine support for change management has either been very coarse grained and thus barely useful, or restricted to formal languages, where automation is possible. In this paper, we report on an effort to extend change management to collections of semi-formal documents which flexibly intermix mathematical formulas and natural language and to integrate it into a semantic publishing system for mathematical knowledge. We validate the long-standing assumption that the semantic annotations in these flexiformal documents that drive the machine-supported interaction with documents can support semantic impact analyses at the same time. But in contrast to the fully formal setting, where adaptations of impacted documents can be automated to some degree, the flexiformal setting requires much more user interaction and thus a much tighter integration into document management workflows.

• A Scalable Module System

  Florian Rabe, Michael Kohlhase

  05/2011;

  Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented mathematical knowledge that needs to be managed to use such syste... [more] Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented mathematical knowledge that needs to be managed to use such systems effectively. While mathematical knowledge management (MKM) "in the small" is well-studied, scaling up to large, highly interconnected corpora remains difficult. We hold that in order to realize MKM "in the large", we need representation languages and software architectures that are designed systematically with large-scale processing in mind. Therefore, we have designed and implemented the MMT language -- a module system for mathematical theories. MMT is designed as the simplest possible language that combines a module system, a foundationally uncommitted formal semantics, and web-scalable implementations. Due to a careful choice of representational primitives, MMT allows us to integrate existing representation languages for formal mathematical knowledge in a simple, scalable formalism. In particular, MMT abstracts from the underlying mathematical and logical foundations so that it can serve as a standardized representation format for a formal digital library. Moreover, MMT systematically separates logic-dependent and logic-independent concerns so that it can serve as an interface layer between computation systems and MKM systems.

• The Planetary System: Executable Science, Technology, Engineering and Math Papers

  Christoph Lange, Michael Kohlhase, Catalin David, Deyan Ginev, Andrea Kohlhase, Bogdan Matican, Stefan Mirea, Vyacheslav Zholudev

  03/2011;

  Executable scientific papers contain not just layouted text for reading. They contain, or link to, machine-comprehensible representations of the scientific findings or experiments they describe. Client-side players can thus enable readers to "check, manipulate and explore the result space"... [more] Executable scientific papers contain not just layouted text for reading. They contain, or link to, machine-comprehensible representations of the scientific findings or experiments they describe. Client-side players can thus enable readers to "check, manipulate and explore the result space". We have realized executable papers in the STEM domain with the Planetary system. Semantic annotations associate the papers with a content commons holding the background ontology, the annotations are exposed as Linked Data, and a frontend player application hooks modular interactive services into the semantic annotations.

• What we understand is what we get: Assessment in Spreadsheets

  Andrea Kohlhase, Michael Kohlhase

  09/2010;

  In previous work we have studied how an explicit representation of background knowledge associated with a specific spreadsheet can be exploited to alleviate usability problems with spreadsheet-based applications. We have implemented this approach in the SACHS system to provide a semantic help system... [more] In previous work we have studied how an explicit representation of background knowledge associated with a specific spreadsheet can be exploited to alleviate usability problems with spreadsheet-based applications. We have implemented this approach in the SACHS system to provide a semantic help system for spreadsheets applications. In this paper, we evaluate the (comprehension) coverage of SACHS on an Excel-based financial controlling system via a "Wizard-of-Oz" experiment. This shows that SACHS adds significant value, but systematically misses important classes of explanations. For judgements about the information contained in spreadsheets, we provide a first approach for an "assessment module" in SACHS. Comment: 11 Pages, 10 Colour Figures

• sTeX+ - a System for Flexible Formalization of Linked Data

  Andrea Kohlhase, Michael Kohlhase, Christoph Lange

  06/2010;

  We present the sTeX+ system, a user-driven advancement of sTeX - a semantic extension of LaTeX that allows for producing high-quality PDF documents for (proof)reading and printing, as well as semantic XML/OMDoc documents for the Web or further processing. Originally sTeX had been created as an invas... [more] We present the sTeX+ system, a user-driven advancement of sTeX - a semantic extension of LaTeX that allows for producing high-quality PDF documents for (proof)reading and printing, as well as semantic XML/OMDoc documents for the Web or further processing. Originally sTeX had been created as an invasive, semantic frontend for authoring XML documents. Here, we used sTeX in a Software Engineering case study as a formalization tool. In order to deal with modular pre-semantic vocabularies and relations, we upgraded it to sTeX+ in a participatory design process. We present a tool chain that starts with an sTeX+ editor and ultimately serves the generated documents as XHTML+RDFa Linked Data via an OMDoc-enabled, versioned XML database. In the final output, all structural annotations are preserved in order to enable semantic information retrieval services. Comment: I-SEMANTICS 2010, September 1-3, 2010, Graz, Austria

• sTeXIDE: An Integrated Development Environment for sTeX Collections

  Constantin Jucovschi, Michael Kohlhase

  05/2010;

  Authoring documents in MKM formats like OMDoc is a very tedious task. After years of working on a semantically annotated corpus of sTeX documents (GenCS), we identified a set of common, time-consuming subtasks, which can be supported in an integrated authoring environment. We have adapted the modula... [more] Authoring documents in MKM formats like OMDoc is a very tedious task. After years of working on a semantically annotated corpus of sTeX documents (GenCS), we identified a set of common, time-consuming subtasks, which can be supported in an integrated authoring environment. We have adapted the modular Eclipse IDE into sTeXIDE, an authoring solution for enhancing productivity in contributing to sTeX based corpora. sTeXIDE supports context-aware command completion, module management, semantic macro retrieval, and theory graph navigation. Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 2010

• Towards MKM in the Large: Modular Representation and Scalable Software Architecture

  Michael Kohlhase, Florian Rabe, Vyacheslav Zholudev

  05/2010;

  MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this ... [more] MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT. Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 2010

• Dimensions of Formality: A Case Study for MKM in Software Engineering

  Andrea Kohlhase, Michael Kohlhase, Christoph Lange

  04/2010;

  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 t... [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 formalized knowledge can be used for enriching interactive document browsing, for enabling multi-dimensional metadata queries over documents and collections, and for exporting Linked Data to the Semantic Web and thus enabling further reuse. Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 2010

• Publishing Math Lecture Notes as Linked Data

  Catalin David, Michael Kohlhase, Christoph Lange, Florian Rabe, Nikita Zhiltsov, Vyacheslav Zholudev

  04/2010;

  We mark up a corpus of LaTeX lecture notes semantically and expose them as Linked Data in XHTML+MathML+RDFa. Our application makes the resulting documents interactively browsable for students. Our ontology helps to answer queries from students and lecturers, and paves the path towards an integration... [more] We mark up a corpus of LaTeX lecture notes semantically and expose them as Linked Data in XHTML+MathML+RDFa. Our application makes the resulting documents interactively browsable for students. Our ontology helps to answer queries from students and lecturers, and paves the path towards an integration of our corpus with external sites. Comment: 7th Extended Semantic Web Conference (http://www.eswc2010.org), Demo Track

• sTeXIIS: An Integrated Development Environment for sTeX Collections.

  Constantin Jucovschi, Michael Kohlhase

  Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5-10, 2010. Proceedings; 01/2010

• Publishing Math Lecture Notes as Linked Data.

  Catalin David, Michael Kohlhase, Christoph Lange, Florian Rabe, Nikita Zhiltsov, Vyacheslav Zholudev

  The Semantic Web: Research and Applications, 7th Extended Semantic Web Conference, ESWC 2010, Heraklion, Crete, Greece, May 30 - June 3, 2010, Proceedings, Part II; 01/2010

• S

  Andrea Kohlhase, Michael Kohlhase, Christoph Lange

  Proceedings the 6th International Conference on Semantic Systems, I-SEMANTICS 2010, Graz, Austria, September 1-3, 2010; 01/2010

• Dimensions of Formality: A Case Study for MKM in Software Engineering.

  Andrea Kohlhase, Michael Kohlhase, Christoph Lange

  Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5-10, 2010. Proceedings; 01/2010

• Cut-Simulation and Impredicativity

  Christoph Benzmueller, Chad E. Brown, Michael Kohlhase

  03/2009;

  We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type theory -- is like adding cut. The phenomenon equal... [more] We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type theory -- is like adding cut. The phenomenon equally applies to prominent axioms like Boolean- and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.
• 4.88

  Impact points

  Semantic Knowledge Management for Education

  A. Kohlhase, M. Kohlhase

  Proceedings of the IEEE. 07/2008;

  ldquoSemantic technologiesrdquo are touted as the next big wave in educational technology and as the solution to many problems in this arena. Interdisciplinary work between the fields of knowledge management (KM) and educational technology (ET) is booming. But the crop of actual systems and semantic... [more] ldquoSemantic technologiesrdquo are touted as the next big wave in educational technology and as the solution to many problems in this arena. Interdisciplinary work between the fields of knowledge management (KM) and educational technology (ET) is booming. But the crop of actual systems and semantically enhanced learning objects is still meager, maybe because KM and EL are lacking a consensus on the underlying notions, e.g., of ldquosemantics,rdquo yielding specific problems in their interplay. In this paper, we look at semantic educational technologies and draw conclusions for their approach in KM. In particular, we (re)evaluate the notions of semantics, knowledge, and learning; their role for learning materials in ET; and how they interact with the contexts involved in the learning/teaching process. Based on this, we distill a list of conditions the underlying knowledge representation format must fulfil to support these. As these conditions are still rather abstract, we show how they can be realized in a concrete language design, taking in our open mathematical documents format OMDoc as a point of departure.

• Information Society Technologies

  A. Asperti, M. Kohlhase, C. Sacerdoti Coen

  05/2004;

  This report comes out of the attempt to translate the HELM CIC format into OMDoc by XslT style sheets. The experiment and the resulting style sheets are covered in the companion document D2c of this report. These style sheets transform the the low-level XML description of the library of the Coq Proo... [more] This report comes out of the attempt to translate the HELM CIC format into OMDoc by XslT style sheets. The experiment and the resulting style sheets are covered in the companion document D2c of this report. These style sheets transform the the low-level XML description of the library of the Coq Proof Assistant to the version of OMDoc described in this report. Currently, the style sheets only cover a part of the ultimate transformation, covered by the original HELM format. This part consists in adding inner types (as content-MathML expressions) to the -terms exported from Coq and transforming the proof structure. The generation of natural language, line-breaking considerations, etc. will be implemented later in the task T2.5

• A Time Calculus for Natural Language

  Benjamin Han, Michael Kohlhase

  10/2003;

  Automatic extraction and reasoning of temporal properties in a natural language discourse has not seen wide use in practical systems due to its demand of a rich and compositional, yet inference-friendly representation of time. We address the problem by proposing a time calculus within the framework ... [more] Automatic extraction and reasoning of temporal properties in a natural language discourse has not seen wide use in practical systems due to its demand of a rich and compositional, yet inference-friendly representation of time. We address the problem by proposing a time calculus within the framework of temporal constraint satisfaction problems (TCSP) [4], based on our study of the Penn Treebank corpora [11]. The formulation models temporal expressions as a two-level TCSP, thus enabling a system to answer a wide range of temporal-related queries.

• System Description: Analytica 2

  Edmund Clarke, Michael Kohlhase, Klaus Sutner

  10/2003;

  The Analytica system is a theorem proving system for 19 century mathematics written on top of the Mathematica computer algebra system. It was developed in the early 1990's by X. Zhao and E. Clarke and has since been dormant. We describe recent work to resurrect the theorem prover and port it to ... [more] The Analytica system is a theorem proving system for 19 century mathematics written on top of the Mathematica computer algebra system. It was developed in the early 1990's by X. Zhao and E. Clarke and has since been dormant. We describe recent work to resurrect the theorem prover and port it to newer versions of Mathematica. The new system Analytica 2 can still prove the same theorems, but has been signi cantly cleaned up. The code has been restructured and documented, the declarative knowledge has been separated from a logical kernel, and the system is being made available as a MathWeb service.