The reasoning power of human-oriented plan-based reasoning systems is primarily derived from their domain-specific problem solving knowledge. Such knowledge is, however, intrinsically incomplete. In order to model the human ability of adapting existing methods to new situations we present in this work a declarative approach for representing methods, which can be adapted by so-called meta-methods. Since apparently the success of this approach relies on the existence of general and strong meta-methods, we describe several meta-methods of general interest in detail by presenting the problem solving process of two familiar classes of mathematical problems. These examples should illustrate our philosophy of proof planning as well: besides planning with the current repertoire of methods, the repertoire of methods evolves with experience in that new ones are created by meta-methods which modify existing ones.

ion, Reformulation, and Approximation, SARA-95, Ville d'Esterel, Canada, 1995, forthcoming. Adapting the Diagonalization Method by Reformulations Xiaorong Huang Manfred Kerber Lassaad Cheikhrouhou Fachbereich Informatik Universitat des Saarlandes D-66041 Saarbrucken Germany fhuang---kerber---lassaadg@cs.uni-sb.de Abstract Extending the plan-based paradigm for automated theorem proving, we developed in previous work a declarative approach towards representing methods in a proof planning framework to support their mechanical modification. This paper presents a detailed study of a class of particular methods, embodying variations of a mathematical technique called diagonalization. The purpose of this paper is mainly twofold. First we demonstrate that typical mathematical methods can be represented in our framework in a natural way. Second we illustrate our philosophy of proof planning: besides planning with a fixed repertoire of methods, meta-methods create new methods by modifying e...