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Abstract: Many mathematical proofs are hard to generate for humans and even harder for automated theorem provers. Classical techniques of automated theorem proving involve the application of basic rules, of builtin special procedures, or of tactics. Melis (Melis 1993) introduced a new method for analogical reasoning in automated theorem proving. In this paper we show how the derivational analogy replay method is related and extended to encompass analogy-driven proof plan construction. The method is... (Update)
Context of citations to this paper: More
...x i of f are mapped to arguments x ij of f 0 . and general reformulation that has been used in many examples documented in [Mel93b, MV94, HKKR94] Moreover, the particular Heine Borel example was chosen independently in [Ble95a] The objection that every new example would...
.... this method can cope with the analogies in the mentioned textbook and is even able to deal with more complicated mathematical theorems [99] such as a non trivial Heine Borel theorem. This example has been proposed in [12] as a challenging example for theorem proving by...
Cited by: More
Theorem Proving by Analogy - A Compelling Example - Melis (1995) (Correct)
Modification in Analogy-Driven Proof-Plan Construction - Melis (1995) (Correct)
How Mathematicians Prove Theorems - Melis (1994) (Correct)
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0.5: Decidable Reasoning in Terminological Knowledge.. - Buchheit, Donini.. (1993) (Correct)
0.4: Analogy in Problem Solving - Melis, Veloso (Correct)
0.4: The Heine-Borel Challenge Problem - Melis (1998) (Correct)
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0.5: Analogy as a Control Strategy in Theorem Proving - Melis, Whittle (1997) (Correct)
0.4: Analogical Reasoning with a Hybrid Knowledge Base - Kerber, Melis, Siekmann (Correct)
0.4: Local and Global Feedback - Melis, Ullrich (Correct)
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6: The use of explicit plans to guide inductive proofs - Bundy - 1988
6: Methods - the basic units for planning and verifying proofs - Huang, Kerber et al. - 1992
6: Derivational analogy: a theory of reconstructive problem solving and expertise a.. (context) - Carbonell - 1986
BibTeX entry: (Update)
E. Melis and M.M. Veloso. Analogy makes proofs feasible. In D. Aha, editor, AAAI-94 Workshop on Case Based Reasoning, pages 13--17, Seattle, 1994. http://citeseer.ist.psu.edu/melis94analogy.html More
@misc{ melis94analogy,
author = "E. Melis and M. Veloso",
title = "Analogy makes proofs feasible",
text = "E. Melis and M.M. Veloso. Analogy makes proofs feasible. In D. Aha, editor,
AAAI-94 Workshop on Case Based Reasoning, pages 13--17, Seattle, 1994.",
year = "1994",
url = "citeseer.ist.psu.edu/melis94analogy.html" }
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272 Argonne National Laboratory (context) - McCune - 1990
49 Analogy for Automated Reasoning (context) - Owen - 1990
27 A paradigm for reasoning by analogy (context) - Kling - 1971
27 The Psychology of Invention in the Mathematical Field (context) - Hadamard - 1945
27 Case-based Planning: An Integrated Theory of Planning (context) - Hammond - 1986
18 Mathematics and Plausible Reasoning (context) - Polya - 1954
14 Change of representation in theorem proving by analogy - Melis - 1993
10 The use of analogy in automatic proof discovery (context) - Bledsoe - 1986
10 Automated Reasoning: 33 Basic Research Problems (context) - Wos - 1988
7 Wie der Beweis der Vermutung von Baudet gefunden wurde (context) - van der Waerden - 1964
7 A validation based theory of plan modification and reuse (context) - Kambhampati, Hendler - 1992
4 Decomposition techniques and their applications - Melis
2 How to Solve it (context) - Princeton, Polya - 1957
2 Learning by Analogical Reasoning in General Problem Solving (context) - Math, Univ et al. - 1992
2 Elements of the Theory of Computation (context) - Intelligence, Lewis et al. - 1981
1 Introduction to Automata Theory (context) - Yale, Hopcroft et al. - 1979
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.ags.uni-sb.de/publications/deduktion/papers/abstracts.html): More
Reasoning with Assertions and Examples - Kerber, Melis, Siekmann (1993) (Correct)
Computing Parallelism in Discourse - Gardent, Kohlhase (1997) (Correct)
Ωmega: Ein mathematisches Assistenzsystem - Siekmann, Kohlhase, Melis (1998) (Correct)
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