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Proof Planning: A Practical Approach To Mechanized Reasoning In Mathematics
, 1998
"... INTRODUCTION The attempt to mechanize mathematical reasoning belongs to the first experiments in artificial intelligence in the 1950 (Newell et al., 1957). However, the idea to automate or to support deduction turned out to be harder than originally expected. This can not at least be seen in the mul ..."
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Cited by 6 (3 self)
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INTRODUCTION The attempt to mechanize mathematical reasoning belongs to the first experiments in artificial intelligence in the 1950 (Newell et al., 1957). However, the idea to automate or to support deduction turned out to be harder than originally expected. This can not at least be seen in the multitude of approaches that were pursued to model different aspects of mathematical reasoning. There are different dimension according to which these systems can be classified: input language (e.g., ordersorted firstorder logic), calculus (e.g., resolution), interaction level (e.g., batch mode), proof output (e.g., refutation graph), and the purpose (e.g., automated theorem proving) as well as many more subtle points concerning the fine tuning of the proof search. In this contribution the proof planning approach will be presented. Since it is not the mainstream approach to mechanized reasoning, it seems to be worth to look at it in a more principled way and to contrast it to other appro
Progress in Proof Planning: Planning Limit Theorems Automatically
, 1997
"... Proof planning is an alternative methodology to classical automated theorem proving based on exhaustive search that was first introduced by Bundy [8]. The goal of this paper is to extend the current realm of proof planning to cope with genuinely mathematical problems such as the wellknown limit the ..."
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Cited by 2 (1 self)
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Proof planning is an alternative methodology to classical automated theorem proving based on exhaustive search that was first introduced by Bundy [8]. The goal of this paper is to extend the current realm of proof planning to cope with genuinely mathematical problems such as the wellknown limit theorems first investigated for automated theorem proving by Bledsoe. The report presents a general methodology and contains ideas that are new for proof planning and theorem proving, most importantly ideas for search control and for the integration of domain knowledge into a general proof planning framework. We extend proof planning by employing explicit controlrules and supermethods. We combine proof planning with constraint solving.