Systematic Mathematical Theory Exploration within the Theorema System: Case Studies

Ziel

Systematic mathematical theory exploration is at the heart of the emerging field of mathematical knowledge management. Bruno Buchberger has recently proposed the 4 threads Theory Exploration Model. The 4 threads are: - the ideas thread (consisting of conc entrated mathematical knowledge in the form of definition, theorem, algorithm, problem schemes); - the theory thread (definitions, theorems, problems, algorithms); - the reasoning objects thread (proof objects, solution objects, simplification objects); - the reasoners thread (provers, solvers, simplifiers and their correctness).The aim of this project is to apply this model in two important case studies, in the Theorema system: systematic exploration of the theory of tuples, and systematic exploration of t he theory of Groebner bases. This will result in the build-up of the respective theories and, as a side-effect, the implementation of exploration tools in the Theorema system.

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natural sciencesmathematics

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INSTITUTE E-AUSTRIA TIMISOARA

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B-dul Cornel Coposu 4
TIMISOARA
Rumänien

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