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Journals and Conferences
Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theorema-supported mathematical theory exploration by a case study (the automated synthesis of an algorithm for the construction of Gröbner Bases) and gives an overview… (More)
Theorema 2.0 stands for a re-design 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… (More)
Interactive software systems that are designed to offer proving and computing facilities at the same time face the problem of evaluation of formulae: In the situation of computing, a formula given to the system should be evaluated whereas in the situation of proving the formula should be kept unevaluated. Also, in the Theorema project we use the same… (More)
The world of mathematical domains is structured hierarchically. There are elementary domains and there are well– known techniques how to build up new domains from existing ones. Which of the domains to view as the actual basis of the hierarchy is the freedom of the mathematician who wants to work with these domains and it depends of course on the intention… (More)
Novel auction schemes are constantly being designed. Their design has significant consequences for the allocation of goods and the revenues generated. But how to tell whether a new design has the desired properties, such as efficiency, i.e. allocating goods to those bidders who value them most? We say: by formal, machine-checked proofs. We investigated the… (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-ComputeSolve”-paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.
Theoretical economics makes use of strict mathematical methods. For instance, games as introduced by von Neumann and Morgenstern allow for formal mathematical proofs for certain axiomatized economical situations. Such proofs can—at least in principle—also be carried through in formal systems such as Theorema. In this paper we describe experiments carried… (More)
Theorema 2.0 stands for a re-design 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.
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… (More)