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Abstract: We present a personal view and strategy for algorithm-supported mathematical theory exploration and draw some conclusions for the desirable functionality of future mathematical software systems. The main points of emphasis are: The use of schemes for bottom-up mathematical invention, the algorithmic generation of conjectures from failing proofs for top-down mathematical invention, and the possibility to program new reasoners within the logic on which the reasoners work... (Update)
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0.6: Theory Exploration with Theorema - Buchberger (2000) (Correct)
0.5: Predicate Logic with Sequence Variables and Sequence.. - Kutsia, Buchberger (2004) (Correct)
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BibTeX entry: (Update)
B. Buchberger. Algorithm--Supported Mathematical Theory Exploration: A Personal View and Strategy. In: J. Campbell (ed.), Proceedings of AISC 2004 (7th Conference on Artifiicial Intelligence and Symbolic Computation, Sep. 22--24, 2004, Research Institute for Symbolic Computation, Hagenberg, Austria), Lecture Notes in Artificial Intelligence, Springer, to appear 2004. http://citeseer.ist.psu.edu/buchberger04algorithmsupported.html More
@misc{ buchberger04algorithmsupported,
author = "B. Buchberger",
title = "Algorithm--Supported Mathematical Theory Exploration: A Personal View and
Strategy",
text = "B. Buchberger. Algorithm--Supported Mathematical Theory Exploration: A
Personal View and Strategy. In: J. Campbell (ed.), Proceedings of AISC 2004
(7th Conference on Artifiicial Intelligence and Symbolic Computation, Sep.
22--24, 2004, Research Institute for Symbolic Computation, Hagenberg, Austria),
Lecture Notes in Artificial Intelligence, Springer, to appear 2004.",
year = "2004",
url = "citeseer.ist.psu.edu/buchberger04algorithmsupported.html" }
Citations (may not include all citations):592 Introduction to HOL: A Theorem Proving Environment for Highe.. (context) - Gordon, Melham - 1993
191 Lego proof development system: User's manual (context) - Luo, Pollack - 1992
145 Isabelle: the next 700 theorem provers (context) - Paulson - 1990
85 The ALF proof editor and its proof engine (context) - Magnusson, Nordstrom - 1994
63 Elf: A meta-language for deductive systems (context) - Pfenning - 1995
47 Logical frameworks - Pfenning - 2001
21 The Theorema project: A progress report (context) - Buchberger, Dupre et al. - 2000
20 The mathematical language automath (context) - de Bruijn - 1970
11 OMDoc: Towards an internet standard for the administration - Kohlhase - 2001
9 Algorithm synthesis by lazy thinking: Examples and implement.. (context) - Buchberger, Craciun - 2003
4 Calculi of meta-variables (context) - Sato, Sakurai et al. - 2003
4 Predicate logic with sequence variables and sequence functio.. - Kutsia, Buchberger - 2004
3 Implementing Mathematics Using the Nuprl Proof Development S.. (context) - Constable - 1986
2 Towards the automated synthesis of a Grobner bases algorithm (context) - Buchberger - 2004
2 volume 2594 of Lecture Notes in Computer Science (context) - Asperti, Buchberger et al. - 2003
[Article contains additional citations not shown here]
Documents on the same site (http://www.risc.uni-linz.ac.at/people/buchberg/refereed_publications.html): More
Symbolic Computation: Computer Algebra and Logic - Buchberger (1996) (Correct)
Algorithm Invention And Verification By Lazy Thinking - BUCHBERGER (2003) (Correct)
An Environment for Building Mathematical Knowledge Libraries - Piroi, Buchberger (2004) (Correct)
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