Papers by Wolfgang Windsteiger
arXiv (Cornell University), Jul 5, 2013
Theorema 2.0 stands for a redesign including a complete re-implementation of the Theorema system,... more Theorema 2.0 stands for a redesign including a complete re-implementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this paper, we present the first prototype of a graphical user interface (GUI) for the new system. It heavily relies on powerful interactive capabilities introduced in recent releases of the underlying Mathematica system, most importantly the possibility of having dynamic objects connected to interface elements like sliders, menus, check-boxes, radio-buttons and the like. All these features are fully integrated into the Mathematica programming environment and allow the implementation of a modern user interface.
Lecture Notes in Computer Science, 2017
In earlier work presented at CICM, four theorem provers (Isabelle, Mizar, Hets/CASL/TPTP, and The... more In earlier work presented at CICM, four theorem provers (Isabelle, Mizar, Hets/CASL/TPTP, and Theorema) were compared based on a case study in theoretical economics, the formalization of the landmark Theorem of Vickrey in auction theory. At the time of this comparison the Theorema system was in a state of transition: The original Theorema system (Theorema 1) had been shut down by the Theorema group and the successor system Theorema 2.0 was just about to be launched. Theorema 2.0 participated in the competition, but only parts of the system were ready for use. In particular, the new reasoning engines had not been set up, so that some of the results in the system comparison had to be extrapolated from experience we had with Theorema 1. In this paper, we now want to compare a complete formalization of Vickrey's Theorem in Theorema 2.0 with the original formalization in Isabelle. On the one hand, we compare the mathematical setup of the two theories and, on the other hand, we also give an overview on statistical indicators, such as number of auxiliary lemmas and the total number of proof steps needed for all proofs in the theory. Last but not least, we present a shorter version of proof of the main theorem in Isabelle.
Electronic Proceedings in Theoretical Computer Science, 2021
We report on several scenarios of using automated theorem proving software in university educatio... more We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial intelligence. The purpose of using logicsoftware in our teaching is not to teach students the proper use of a particular piece of software. In contrast, we try to employ certain software in order to spark students' motivation and to support their understanding of logic principles they are supposed to understand after having passed the course. In a sense, we try to let the software act as a logic-tutor, the software is not an additional subject we teach.
Proceedings of the 12th International Conference on Computer Supported Education, 2020
Nowadays, logic plays an ever-increasing role in modern computer science, in theory as well as in... more Nowadays, logic plays an ever-increasing role in modern computer science, in theory as well as in practice. Logic forms the foundation of the symbolic branch of artificial intelligence and from an industrial perspective, logic-based verification technologies are crucial for major hardware and software companies to ensure the correctness of complex computing systems. The concepts of computational logic that are needed for such purposes are often avoided in early stages of computer science curricula. Instead, classical logic education mainly focuses on mathematical aspects of logic depriving students to see the practical relevance of this subject. In this paper we present our experiences with a novel design of a first-semester bachelor logic course attended by about 200 students. Our aim is to interlink both foundations and applications of logic within computer science. We report on our experiences and the feedback we got from the students through an extensive survey we performed at the end of the semester.
Introduction We present an environment for learning and teaching mathematics that aims at inspiri... more Introduction We present an environment for learning and teaching mathematics that aims at inspiring the creative potential of students by enabling the learners to perform various kinds of interactive computer experiments during their learning process. Computer interactions are both of visual and purely formal mathematical nature, where the computer-algebra system Mathematica powers the visualization of mathematical concepts and the tools provided by the mathematical assistant system Theorema, which is also based on Mathematica, are used for the formal counterparts. We present case studies on equivalence relations and polynomial interpolation, in which we demonstrate the entire bandwidth of computer-support that we envision for modern learning environments for mathematics.
We present a case study using the Theorema system to explore an algorithm for polynomial interpol... more We present a case study using the Theorema system to explore an algorithm for polynomial interpolation. The emphasis of the case study lies on formulating mathematical knowledge in one language that appears in its syntax close to common mathematical language but is precise enough to formulate all details necessary for proving. Moreover, the language allows the computation of concrete examples
Electronic Proceedings in Theoretical Computer Science, 2013
Theorema 2.0 stands for a redesign including a complete re-implementation of the Theorema system,... more Theorema 2.0 stands for a redesign including a complete re-implementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this paper, we present the first prototype of a graphical user interface (GUI) for the new system. It heavily relies on powerful interactive capabilities introduced in recent releases of the underlying Mathematica system, most importantly the possibility of having dynamic objects connected to interface elements like sliders, menus, check-boxes, radio-buttons and the like. All these features are fully integrated into the Mathematica programming environment and allow the implementation of a modern user interface.
Lecture Notes in Computer Science, 2014
Theorema 2.0 stands for a redesign including a complete reimplementation of the Theorema system, ... more Theorema 2.0 stands for a redesign including a complete reimplementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this talk, we want to present the current status of the new implementation, in particular the new user interface of the system.
Lecture Notes in Computer Science, 2013
Where a licence is displayed above, please note the terms and conditions of the licence govern yo... more Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version. Take down policy While the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.
Undergraduate Texts in Mathematics
ABSTRACT This appendix will discuss several computer algebra systems that can be used in conjunct... more ABSTRACT This appendix will discuss several computer algebra systems that can be used in conjunction with the text. We will describe AXIOM, Maple, Mathematica and REDUCE in some detail, and then mention some other systems. These are all amazingly powerful programs, and our brief discussion will not do justice to their true capability.
Lecture Notes in Computer Science, 2012
The use of computer-based mathematics tools is widespread in learning. Depending on the way that ... more The use of computer-based mathematics tools is widespread in learning. Depending on the way that these tools assess the learner's solution paths, one can distinguish between automatic assessment tools and semi-automatic assessment tools. Automatic assessment tools directly provide all feedback necessary to the learners, while semi-automatic assessment tools involve the teachers as part the assessment process. They are provided with as much information as possible on the learners' interactions with the tool. How can the teachers know how the learning tools were used and which intermediate steps led to a solution? How can the teachers respond to a learner's question that arises while using a computer tool? Little is available to answer this beyond interacting directly with the computer and performing a few manipulations to understand the tools' state. This paper presents SMALA, a web-based logging architecture that addresses these problems by recording, analyzing and representing user actions. While respecting the learner's privacy, the SMALA architecture supports the teachers by offering fine-grained representations of the learners' activities as well as overviews of the progress of a classroom.
ABSTRACT Almost every Computer Algebra System contains some implementation of the Gröbner bases a... more ABSTRACT Almost every Computer Algebra System contains some implementation of the Gröbner bases algorithm. The present implementation has the following specific features: - The source code is distributed and publically available free of charge. - The library is written in C. - A simple but efficient mechanism of polymorphism is implemented that enables the user to adjust the library to a wide variety of coe cient domains, power product and polynomial representations, admissible orderings, selection strategies for pairs etc. Thus, GROBNER should be a useful tool - for those who want to do research in Grobner bases theory and applications and, hence, need access to all details of the implementation - and also for those who want to apply the algorithm as a black box, possibly as a subalgorithm in a larger implementation, and need high efficiency.
Journal of Symbolic Computation, 2006
This paper presents some fundamental aspects of the design and the implementation of an automated... more This paper presents some fundamental aspects of the design and the implementation of an automated prover for Zermelo-Fraenkel set theory within the Theorema system. The method applies the "Prove-Compute-Solve"-paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.
Analytica V is a theorem proving system that is built on top of the symbolic computation system M... more Analytica V is a theorem proving system that is built on top of the symbolic computation system Mathematica. It was originally designed by E. Clarke and X. Zhao in the early 1990's. We describe here a redesign of the system that extends its abilities to reasoning about some aspects of number theory.
Proc. of Calculemus' …
... Text, B. Buchberger, C. Dupre, T. Jebelean, F. Kriftner, K. Nakagawa, D. Vasaru, and W. Winds... more ... Text, B. Buchberger, C. Dupre, T. Jebelean, F. Kriftner, K. Nakagawa, D. Vasaru, and W. Windsteiger. The THEOREMA project: A progress report. In M. Kerber and M. Kohlhase, editors, Symbolic Computation and Automated Reasoning, pages 98-113. AK Peters, 2001. ...
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
We present an environment for learning and teaching mathematics that aims at inspiring the creati... more We present an environment for learning and teaching mathematics that aims at inspiring the creative potential of students by enabling the learners to perform various kinds of interactive experiments during their learning process. Computer interactions are both of visual and purely formal mathematical nature, where the computer-algebra system Mathematicapowers the visualization of mathematical concepts and the tools provided by the
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Papers by Wolfgang Windsteiger