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Abstract: Woody Bledsoe's last challenge problem is the analogical transfer of the Heine-Borel theorem for real intervals to the two-dimensional case. This could not be solved by the up to then known techniques of analogical theorem proving. The Heine-Borel theorem is a widely known result in mathematics. It is usually stated in the field of real numbers R 1 and similar versions are also true in R 2 , in topology, and in metric spaces. This article shows how analogy-driven proof plan construction is... (Update)
Context of citations to this paper: More
...knowledge and thus make it available to (automated) proof search. Despite a number of achievements (Cheikhrouhou Siekmann, 1998; Melis, 1998; Bundy, van Harmelen, Hesketh, Smaill, 1991) the functionality of HTP still proves to be insufficient, in comparison with the...
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An Interactive Proof Development Environment +.. - Siekmann.. (2000) (Correct)
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1.1: Theorem Proving by Analogy - A Compelling Example - Melis (1995) (Correct)
1.1: Analogy in Problem Solving - Melis, Veloso (Correct)
0.9: A Model of Analogy-Driven Proof-Plan Construction - Melis (1995) (Correct)
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0.5: Proving a Heine-Borel Theorem by Analogy - Melis (Correct)
0.4: When to Prove Theorems by Analogy? - Melis (1996) (Correct)
0.3: Analogy Makes Proofs Feasible - Melis, Veloso (1994) (Correct)
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2: Generating inference-rich discourse through revisions of RST-trees (context) - Horacek - 1998
2: Planning Diagonalization Proofs - Cheikhrouhou - 1997
2: Experiments with proof plans for induction - Bundy, van Harmelen et al. - 1991
BibTeX entry: (Update)
Melis, E. (1998). The Heine-Borel challenge problem. in honor of Woody Bledsoe. http://citeseer.ist.psu.edu/80339.html More
@misc{ melis98heineborel,
author = "E. Melis",
title = "The Heine-Borel challenge problem",
text = "Melis, E. (1998). The Heine-Borel challenge problem. in honor of Woody
Bledsoe.",
year = "1998",
url = "citeseer.ist.psu.edu/80339.html" }
Citations (may not include all citations):272 Argonne National Laboratory (context) - McCune, users et al. - 1990
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97 Experiments with proof plans for induction - Bundy, van Harmelen et al. - 1991
66 How to Solve it (context) - Polya - 1945
49 Analogy for Automated Reasoning (context) - Owen - 1990
42 Reusing proofs - Kolbe, Walther - 1994
42 A model of analogy-driven proof-plan construction - Melis - 1995
38 Non-resolution theorem proving (context) - Bledsoe - 1977
27 The Psychology of Invention in the Mathematical Field (context) - Hadamard - 1945
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18 Mathematics and Plausible Reasoning (context) - Polya - 1954
14 Change of representation in theorem proving by analogy - Melis - 1993
14 A precondition prover for analogy - Bledsoe - 1995
12 Technical Report DAI Research Paper No (context) - Melis, CLAM - 1995
11 Patching proofs for reuse - Kolbe, Walther - 1995
10 Outils pour la Preuve par Analogie (context) - Curien - 1995
10 volume 99 of Heidelberger Taschenbucher (context) - Deussen, Automaten - 1971
10 The use of analogy in automatic proof discovery (context) - Bledsoe - 1986
9 OMEGA: Towards a mathematical assistant (context) - Benzmueller, Cheikhrouhou et al. - 1997
8 Challenge problems in elementary analysis (context) - Bledsoe - 1990
7 Analogies between proofs -- a case study - Melis - 1993
7 Wie der Beweis der Vermutung von Baudet gefunden wurde (context) - van der Waerden - 1964
6 Analogy makes proofs feasible - Melis, Veloso - 1994
4 DECLAME -- eine deklarative Sprache zur Reprasentation von M.. (context) - Sehn - 1995
4 Technical Report Memo ATP (context) - Bledsoe - 1995
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1 A HB1 Lemmata The formalizations of the lemmata used in the .. (context) - Wang, of et al. - 1991
Documents on the same site (http://www.ags.uni-sb.de/~melis/): More
Analogy as a Control Strategy in Theorem Proving - Melis, Whittle (1997) (Correct)
Extensions of Constraint Solving for Proof Planning - Melis, Müller, Zimmer (1999) (Correct)
Two Kinds of Non-Monotonic Analogical Inference - Kerber, Melis (1996) (Correct)
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