”,
”, “to “toprove provethat that
”
” “” => =>“jede/r/s “jede/r/s
”
” => =>“every “every
”
” ......
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Universal Abstract... ... summarizes intended meaning of abstracted work ... stored as language independent highly structured text ... “ontology” provides catalogue of meaningful concepts ... universal grammar a la Montague Semantics provides meaning structure ... hand crafted using special editor
...Localized Expression ... multilingual thesaurus provides translation of individual concepts to structured expressions in individual languages ... individual language grammars provide translations of universal grammatical structures ... together, these two provide a means to systematically express the universal abstract in any local language for which these two localization components are available
Feasibility of Universal Abstracting: Components of Practical Universal Text Creation Showcased by the WebALT Project on Multilingual Mathematics Tutoring WebALT EU Project (2005-2007) Domain: Short mathematical texts and formulas Translations must be guaranteed to be correct Universal grammar: a lambda calculus variant (OpenMath) similar to Montague Semantics of language Universal concepts: K-13 mathematics concepts (OpenMath/MathML); question/command/narrative moods (WebALT) Compositional Semantics: abstraction, function application as compound builders (again, similar to Montague Semantics)
... combined OpenMath as universal semantic grammar of mathematics (both formula and text) ... with OpenMath Content Dictionaries for common mathematical or linguistic concepts ... and Grammatical Framework (GF) generic natural language generation framework for multiple languages ... as well as its own translations of abstract mathematical concepts into individual languages ... to create the tools needed for authoring and distributing highquality multilingual mathematical texts ... including an editor for creating language independent content
References WebALT: http://webalt.math.helsinki.fi Multilingual Delivery of Online Tests in mathematics. Olga Caprotti, Mika Seppälä. Proceedings of Online Educa Berlin 2006. 29 November- 1 December 2006. Berlin, Germany. Multilingual content development for eLearning in Africa. Wanjiku Ng'ang'a. eLearning Africa: 1st Pan-African Conference on ICT for Development, Education and Training. 24-26 May 2006, Addis Ababa, Ethiopia. Multilingual technology for teaching mathematics. Olga Caprotti, Wanjiku Ng'ang'a, Mika Seppälä. International Conference on Engineering Education, Instructional Technology, Assessment, and E-learning (EIAE 05), December 2005. Web Advanced Learning Technologies for Multilingual Mathematics Teaching Support. A. Strotmann, M. Seppälä. ELPUB2005. From Author to Reader: Challenges for the Digital Content Chain. 9th ICCC International Conference on Electronic Publishing. LeuvenHeverlee (Belgium), June 2005. Multilingual Access to Mathematical Exercise Problems. A. Strotmann, W. Ng'ang'a, O. Caprotti. Internet Accessible Mathematical Computation Workshop. ISSAC 2005. July 2005 Chinese Academy of Sciences, Bejing, China. Web Advanced learning Technologies for Assessment in Mathematics. O. Caprotti, L. Carlson, M. Seppälä, A. Strotmann. Recent Research Developments in Learning Technologies, III International Conference on multimedia and ICT's in Education. Formatex (2005). Advanced Language Technologies for Mathematical Markup. O. Caprotti. IMA "Hot Topic" Workshop on The Evolution of Mathematical Communication in the Age of Digital Libraries. December 8-9, 2006, Minneapolis (USA). Final Report of the WebALT Project. O.Caprotti, M. Seppälä. WebALT Deliverable. March 2007. http://webalt.math.helsinki.fi/content/e16/e301/e851/FinalReportoftheWebALTProjectWEBversion_eng.pdf How-to guide for creating multilingual mathematical content. WebALT Consortium. WebALT Project Deliverable D7.4., December 2006. http://webalt.math.helsinki.fi/content/e16/e301/e846/Deliverable7.4_eng.pdf
Languages: Catalan, Dutch, English, Finnish, French, German, Spanish during project; work on additional languages ongoing in several places includes Russiam, Swahili, plus all(!) official European Union languages Language-specific grammars: Generic grammatical constructs + some domainspecific ones; structured by language families (German~Dutch; Romance languages...) Language specific translations of linguistic concepts such as questions / commands, numbers, and of mathematical concepts such as numbers, addition, equality, equation solving... in the form of phrase patterns
Acknowledgments GF (Grammatical Framework) was created by Aarne Ranta, Chalmers University of Technology, who also led development of the generic language generation libraries for GF. The WIRIS/WExEd editor for creating language-independent maths contents was originally created by Maths for More, Barcelona, and adopted to multilingual mathematical text editing as part of the WebALT project. The OpenMath Society's members created the OpenMath universal grammar of mathematics as well as its ontologies of mathematical concepts known as Content Dictionaries. The WebALT project created the corresponding multilingual thesaurus for use with GF, and developed a showcase for high-quality multilingual delivery of brief texts via a universal semantic representation. Its members were: Dr. Mika Seppälä and Lauri Carlson, University of Helsinki - departments of Mathematics and Statistics, of Linguistics, and of Translation; Arjeh Cohen, Technical University of Eindhoven - Dept of Mathematics; Sebastià Xambó, Technical University of Catalonia in Barcelona - Dept of Mathematics; Andreas Strotmann, University of Cologne - Center for Applied Computer Science; and Ramon Eixarch, Maths for More, Barcelona.
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