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A rational reconstruction of a system for experimental mathematics. (English) Zbl 1202.68374

Kauers, Manuel (ed.) et al., Towards mechanized mathematical assistants. 14th symposium, Calculemus 2007, 6th international conference, MKM 2007, Hagenberg, Austria, June 27–30, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73083-5/pbk). Lecture Notes in Computer Science 4573. Lecture Notes in Artificial Intelligence, 13-26 (2007).
Summary: In previous papers we described the implementation of a system which combines mathematical object generation, transformation and filtering, conjecture generation, proving and disproving for mathematical discovery in non-associative algebra. While the system has generated novel, fully verified theorems, their construction involved a lot of ad hoc communication between disparate systems. In this paper we carefully reconstruct a specification of a sub-process of the original system in a framework for trustable communication between mathematics systems put forth by us. It employs the concept of biform theories that enables the combined formalisation of the axiomatic and algorithmic theories behind the generation process. This allows us to gain a much better understanding of the original system, and exposes clear generalisation opportunities.
For the entire collection see [Zbl 1119.68011].

MSC:

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)

Software:

OMRS; MathWeb
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