Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In practice, such systems however face large combinatorial explosion, and therefore include many heuristics and choice points that considerably influence their performance. This is an opportunity for trained machine learning predictors, which can guide the work of such reasoning systems. Conversely, deductive search supported by the notion of logically valid proof allows one to train machine learning systems on large reasoning corpora. Such bodies of proof are usually correct by construction and when combined with more and more precise trained guidance they can be boostrapped into very large corpora, with increasingly long reasoning chains and possibly novel proof ideas. In this paper we provide an overview of several automated reasoning and theorem proving domains and the learning and AI methods that have been so far developed for them. These include premise selection, proof guidance in several settings, AI systems and feedback loops iterating between reasoning and learning, and symbolic classification problems.

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学习引导自动推理：简要调查

自动定理证明器和形式证明助手是通用推理系统，理论上能够证明任意困难的定理，从而解决可简化为数学和逻辑推理的任意问题。然而，在实践中，此类系统面临着巨大的组合爆炸，因此包含许多启发式方法和选择点，这些方法和选择点会极大地影响其性能。这是训练有素的机器学习预测器的机会，它可以指导此类推理系统的工作。相反，由逻辑有效证明概念支持的演绎搜索允许人们在大型推理语料库上训练机器学习系统。这样的证明主体通常通过构造是正确的，当与越来越精确的训练有素的指导相结合时，它们可以被纳入非常大的语料库中，具有越来越长的推理链和可能新颖的证明想法。在本文中，我们概述了几个自动推理和定理证明领域以及迄今为止为它们开发的学习和人工智能方法。其中包括前提选择、多种设置中的证明指导、人工智能系统和推理与学习之间迭代的反馈循环，以及符号分类问题。