1http://www.w3.org/RDF/
tation can mean dieren t things in dieren t contexts, e.g., edge representation, e.g., structural information such as is-aof an exercise. agogical information.
Now, our learning environment ActiveMath [8] is a SeActiveMath’ knowledge representation is based on edge representation is separated from its functionalities. Its mantic Web application for mathematics learning. Its knowlemerging only and where the habits of authors still oppose resented in the OMDoc-language which is an extension of have added for the educational and other purposes of Actheory of quadratic residues.
Math. It focuses on the knowledge representation and its quire additional information to be encoded into the knowlThis article shows how Semantic Web issues such as machinesuch an encoding. knowledge representation meets the above requirements for denition and pedagogical information suc h as the diÆculty ity and inter-operability as well as the representation of pedOpenMath. It describes and substantiates the extensions we tional applications that include the above mentioned reusabilmathematical content representations and those for educaOpenMath [3], a general, standardized, semantic XML-represen( ) = ( )( ) is false in elementary algebra but true in the apb ap pb tation for mathematics. ActiveMath’ functionalities retiveMath. It discusses how content is authored presently current authoring. It summarizes which information is repunderstandable representation, reusability, extensibility, and migration of other representations are tackled in Activein a situation, where tools for semantic representations are incorporate an ontology of the domain or, even better, a alities is desirable. Therefore, the representation needs to same thing, e.g., or 1/2. Conversely, the same presen- 21 eld to experiment with because it is largely formalized prerequisite for multiple services used in education systems knowledge is inherently dieren t from its presentation (e.g., that can access and work with common knowledge sources.
Many educational systems and on-line documents have sentational issues and because mathematics is a relatively pensive and time-consuming task, reusability of the encoded its printed version). Dieren t presentations can mean the their various relationships. Similarly, inter-operability is a to be enhanced by real semantics because mathematical well-structured eld. For mathematics, an ontology needs For Semantic Web applications, mathematics is a good knowledge in dieren t contexts and for dieren t functionbeen produced in recent years. Since the encoding of the and has a clear fundamental semantics independent of preunique and extensible semantics of the domain concepts and domain knowledge for a learning environment is a very ex1. INTRODUCTION Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.
Semantic Web Workshop 2002 Hawai, USA Copyright by the authors. 2. SEMANTIC REPRESENTATION 2.1 Semantics in Mathematical Knowledge and metadata. use the pre-dened environments and macros LATEX for dening OMDoc elements, i.e., structure elements To summarize: as compared with a direct authoring of tractive to authors, it keeps the presentation and looses the information needed for the Semantic Web application. is more familiar to mathematicians even if not strictly LATEX simpler. Although the direct control of the layout of a document by editing the generated PDF-document is very atIf these requirement are met, our tool automatically converts the restricted sources via QMath to OMDoc. LATEX representation and thus destroys the semantic and metadata OMDoc in QMath, authoring in a restricted and augmented