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  • ThEdu'14 - Theorem Provers Components for Educational Software

    ThEdu'14 Web-page

    THedu is a forum to gather the research communities for Automated Theorem Proving (ATP), Interactive Theorem Proving (ITP) as well as for Computer Algebra Systems (CAS), Dynamic Geometry Systems (DGS) and Mathematical Education. The goal of this union is to combine and focus systems of these areas and to enhance existing educational software as well as studying the design of the next generation of mechanised mathematics assistants.

    Elements for next-generation assistants include:

    • Declarative Languages for Problem Solution: education in applied sciences and in engineering is mainly concerned with problems, which are understood as operations on elementary objects to be transformed to an object representing a problem solution. Preconditions and post-conditions of these operations can be used to describe the possible steps in the problem space; thus, ATP-systems can be used to check if an operation sequence given by the user does actually present a problem solution. Such "Problem Solution Languages" encompass declarative proof languages like Isabelle/Isar or Coq's Mathematical Proof Language, but also more specialised forms such as, for example, geometric problem solution languages that express a proof argument in Euclidean Geometry or languages for graph theory.
    • Consistent Mathematical Content Representation: libraries of existing ITP-Systems, in particular those following the LCF-prover paradigm, usually provide logically coherent and human readable knowledge. In the leading provers, mathematical knowledge is covered to an extent beyond most courses in applied sciences. However, the potential of this mechanised knowledge for education is clearly not yet recognised adequately: renewed pedagogy calls for enquiry-based learning from concrete to abstract --- and the knowledge's logical coherence supports such learning: for instance, the formula 2.Pi depends on the definition of reals and of multiplication; close to these definitions are the laws like commutativity etc. Clearly, the complexity of the knowledge's traceable interrelations poses a challenge to usability design.
    • User-Guidance in Step-wise Problem Solving: Such guidance is indispensable for independent learning, but costly to implement so far, because so many special cases need to be coded by hand. However, TP technology makes automated generation of user-guidance reachable: declarative languages as mentioned above, novel programming languages combining computation and deduction, methods for automated construction with ruler and compass from specifications, etc --- all these methods 'know how to solve a problem'; so, using the methods' knowledge to generate user-guidance mechanically is an appealing challenge for ATP and ITP, and probably for compiler construction.
    • Pedagogical strategies: Using TP technologies in learning environments call for strategies for linking and adapting the availble tools for specific educational needs and new methods for the management of mathematical knowledge capable of filling the gap between repositories and end-user system and new visual and/or natural language interfaces to allow the use of rigorous reasoning methods and tools.

    In principle, mathematical software can be conceived as models of mathematics: The challenge addressed by this workshop is to provide appealing models for mathematics assistants which are interactive and which explain themselves such that interested students can independently learn by inquiry and experimentation.

    Programme Committee

    • Francisco Botana, University of Vigo at Pontevedra, Spain
    • Roman HaĊĦek, University of South Bohemia, Czech Republic
    • Filip Maric, University of Belgrade, Serbia
    • Walther Neuper, Graz University of Technology, Austria (co-chair)
    • Pedro Quaresma, University of Coimbra, Portugal (co-chair)
    • Vanda Santos, CISUC, Portugal
    • Wolfgang Schreiner, Johannes Kepler University, Austria
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Last modified: December 19 2016 18:02:46 CET