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  Reasoning at Multiple Levels of Abstraction

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by Robert Vero
http://www.cs.unm.edu/~moore/tr/00-10/multiplelevels.ps.gz
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Abstract:

Abstract. In order to be successful in complex domains involving hierarchies of dened terms, an automated reasoning program must be able to reason eectively at multiple levels of abstraction. At a minimum, this requires appropriate problem representations and good search strategies. Ideally, the reasoning program reasons at high levels of abstraction when possible and appeals to arguments at lower levels of abstraction only as necessary. In this article, we describe our early experiences developing representations and search strategies for an application of automated reasoning to a problem domain from theoretical computer science. We then summarize some of the approaches we are considering to permit the automated reasoning program to reason eectively at multiple levels of abstraction. 1

Citations

1396 Applied Dynamic Programming – Bellman, Dreyfus - 1962
491 A Computational Logic – Boyer, Moore - 1979
388 Planning in a hierarchy of abstraction spaces – Sacerdoti - 1974
263 Otter 3.0 Reference Manual and Guide – McCune - 1994
154 A Theory of Abstraction – Giunchiglia, Walsh - 1992
99 Solution of the Robbins problem – McCune - 1997
46 Automatic Deduction with Hyper-Resolution – Robinson - 1965
43 Automated development of fundamental mathematical theories – Quaife - 1992
31 DISCOUNT: A Distributed and Learning Equational Prover – Denzinger, Kronenburg, et al. - 1997
28 Complexity and related enhancements for automated theorem-proving programs – McCharen, Overbeek, et al. - 1976
17 Set theory in first-order logic: Clauses for Gödel’s axioms – Boyer, Lusk, et al. - 1986
15 Abstraction mappings in mechanical theorem proving – Plaisted - 1980
12 The linked inference principle, i: The formal treatment – Veroff, Wos - 1992
9 The linked inference principle, II: the user's viewpoint – Wos, Vero, et al. - 1984
8 ROO: a parallel theorem prover – Lusk, McCune, et al. - 1992
6 Exploitation of parallel processing for implementing high-performance deduction systems – Jindal, Overbeek, et al. - 1992
6 A common schema for dynamic programming and branch and bound algorithms – Helman - 1989
3 Man-machine Theorem Proving in Graph Theory – Cvetkovic, Pevac - 1988
2 Gazing: An Approach to the Problem of De and Lemma Use – Barker-Plummer - 1992
1 The application of automated reasoning to formal models of combinatorial optimization – Helman, Vero
1 Metalevel Reasoning for Controlling Automated Reasoning Programs – Henschen - 1997
1 Parallel Uni Theory and Implementations – Sibai - 1990
1 Heterogeneous Parallel Deduction Systems," Fifth Generation Computer Systems – Sutclie - 1992
1 The Problem of De Expansion and Contraction – Wos - 1987