E. Melis and A. Bundy. Planning and proof planning. In S. Biundo, editor, ECAI-96 Workshop on Cross-Fertilization in Planning, pages 37-40, Budapest, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... it might be a good idea to search for proofs via a proof plan rather than directly on calculus level (section 2) Also I am going to describe what a proof planning system needs to provide in order to instantiate these hopes (section 3) Then I am going to argue briefly that methods as described in [Bun88, MB96, HKRS94, Seh95] can be used to implement the relevant features. 2 Motivation Traditional Automated Theorem Proving (ATP) suffers from search in exponential search trees. In case one uses higher order object languages which seems to be appropriate for most interesting tasks there are further complications ....

E. Melis and A. Bundy. Planning and proof planning. In S. Biundo, editor, ECAI-96 Workshop on Cross-Fertilization in Planning, Budapest, 1996. available from http://jswww.cs.uni-sb.de/melis/.

....in [8] as an alternative to the methodology of classical automated theorem proving. It employs high level planning operators rather than calculus level rules and global control as opposed to the more local search heuristics which are used for search control in automated theorem proving (see, e.g. [28]) However, there are classes of theorems that are difficult or impossible to prove by state of the art proof planners such as CL4M[10] or OMEGA [3] For instance, the limit theorem LIM was beyond the capabilities of theorem provers and proof planners. For many problems, the available control ....

E. Melis and A. Bundy. Planning and proof planning. In S. Biundo, editor, ECAI-96 Workshop on Cross-Fertilization in Planning, pages 37-40, Budapest, 1996.

....by Bundy (1988) for inductive proofs. As opposed to classical theorem proving, proof planning employs high level planning operators rather than calculus level rules and global control rather than the more local search heuristics which are used for search control in automated theorem proving, see (Melis Bundy 1996). The rst proof planner, CL A M(Bundy et al. 1991) has successfully planned inductive proofs and some proof planning attempts have previously been performed in the OMEGA system (Benzmueller et al. 1997) 2 . This work was supported by the Deutsche Forschungsgemeinschaft, SFB 378 y ....

....the eventually resulting assumption is marked by a focus before applying UNWRAPHYP. However, this anticipation may not be fully reliable and the subgoals in LIST that arise during the expansion cannot be predicted. In a multi strategy planner as described in (Kambhampati, Knoblock, Yang 1995; Melis 1996), the expansion of supermethods can be a re nement strategy. This expansion strategy yields the subplan that is introduced into the plan at a hierarchically lower level. The expansion strategy can be invoked exibly depending on the planning state and history as well as on resources and properties ....

Melis, E., and Bundy, A. 1996. Planning and proof planning. In Biundo, S., ed., ECAI-96 Workshop on Cross-Fertilization in Planning, 37-40.

.... Proof planning, introduced by Bundy [6] for inductive theorem proving, is a potential solution of the super exponential search problem because it employs global search control as opposed to the more local search heuristics which are used for search control in automated theorem proving (see, e.g. [18]) This global search control corresponds to mathematicians sense of direction that Bledsoe demanded to use in automated theorem proving in 1986 [3] pay attention to mathematician s great deal of direction rather than cover the eyes with blinders and hunt through a cornfield for a ....

E. Melis and A. Bundy. Planning and proof planning. In S. Biundo, editor, ECAI-96 Workshop on Cross-Fertilization in Planning, pages 37-- 40, Budapest, 1996.

....Proof planning is an alternative to classical theorem proving working at the calculus level, e.g. of resolution. A motivation for proof planning is the fact that mathematicians tend to plan proofs. We give some essentials of proof planning only. For more details about the state of the art see [26]. For proof planning two roads join, 1) the use of tactics and (2) meta level control. As opposed to traditional automated theorem that applies calculus level inference rules, i.e. low level inferences, proof planning relies on tactics [14] Tactics are procedures that produce a (not necessarily ....

E. Melis and A. Bundy. Planning and proof planning. In S. Biundo, editor, ECAI-96 Workshop on Cross-Fertilization in Planning, pages 37--40, Budapest, 1996.

....in [8] as an alternative to the methodology of classical automated theorem proving. It employs high level planning operators rather than calculus level rules and global control as opposed to the more local search heuristics which are used for search control in automated theorem proving (see, e.g. [29]) However, there are classes of theorems that are difficult or impossible to prove by stateof the art proof planners such as CL A M[10] or OMEGA [3] For instance, the limit theorem LIM is beyond the capabilities of current theorem provers and proof planners. For many problems, the available ....

E. Melis and A. Bundy. Planning and proof planning. In S. Biundo, editor, ECAI-96 Workshop on Cross-Fertilization in Planning, pages 37--40, Budapest, 1996.

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