Progress in Proof Planning:Planning Limit Theorems Automatically

  • Proof planning is an alternative methodology to classical automated theorem prov-ing based on exhausitve search that was first introduced by Bundy [8]. The goal ofthis paper is to extend the current realm of proof planning to cope with genuinelymathematical problems such as the well-known limit theorems first investigated for au-tomated theorem proving by Bledsoe. The report presents a general methodology andcontains ideas that are new for proof planning and theorem proving, most importantlyideas for search control and for the integration of domain knowledge into a general proofplanning framework. We extend proof planning by employing explicit control-rules andsupermethods. We combine proof planning with constraint solving. Experiments showthe influence of these mechanisms on the performance of a proof planner. For instance,the proofs of LIM+ and LIM* have been automatically proof planned in the extendedproof planner OMEGA.In a general proof planning framework we rationally reconstruct the proofs of limittheorems for real numbers (IR) that were first computed by the special-purpose programreported in [6]. Compared with this program, the rational reconstruction has severaladvantages: It relies on a general-purpose problem solver; it provides high-level, hi-erarchical representations of proofs that can be expanded to checkable ND-proofs; itemploys declarative contol knowledge that is modularly organized.

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Verfasserangaben:Erica Melis
URN (Permalink):urn:nbn:de:hbz:386-kluedo-3804
Schriftenreihe (Bandnummer):SEKI Report (97,8)
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:1999
Jahr der Veröffentlichung:1999
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):03.04.2000
Fachbereiche / Organisatorische Einheiten:Fachbereich Informatik
DDC-Sachgruppen:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011