Reasoning Heuristics for the Theorem-Proving Platform Rodin/Event-B

Jacobus Gideon Ackermann, John Andrew van der Poll
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引用次数: 2

Abstract

Developments in formal- and mathematical logic; and computing the past couple of decades have paved the way for the automation of deductive reasoning. However, despite theoretical and technological advances in computing, the rapid growth in the search space for complex proofs where the reasoner explores the consequences of irrelevant information, remains problematic. The challenge of a combinatorial explosion of the search space can in many cases be addressed by heuristics. Consequently, in this paper we investigate the extent to which heuristics may usefully be applied in discharging complex set-theoretic proof obligations using the hybrid reasoning environment, Rodin/Event-B. On the strength of our experiments, we develop a set of heuristics to aid the theorem-proving environment in finding proofs for set-theoretic problems which could not be obtained using the default settings. A brief exposition of related work in this area is presented towards the end of the paper.
定理证明平台Rodin/Event-B的推理启发式
形式逻辑和数学逻辑的发展;过去几十年的计算为演绎推理的自动化铺平了道路。然而,尽管计算在理论和技术上取得了进步,但在推理者探索不相关信息的结果的复杂证明的搜索空间的快速增长仍然存在问题。在许多情况下,搜索空间的组合爆炸的挑战可以通过启发式来解决。因此,在本文中,我们研究了启发式在使用混合推理环境Rodin/Event-B履行复杂集合论证明义务时可能有效应用的程度。在实验的基础上,我们开发了一套启发式方法,以帮助定理证明环境找到使用默认设置无法获得的集合论问题的证明。本文最后简要介绍了这一领域的相关工作。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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