SHF: Small: WLoS: Without Loss of Satisfaction

将传统上由人类执行的活动（例如装配线工作或组织任务）自动化的关键是将这些活动分解为许多易于处理的简单步骤。虽然这种方法也已用于自动化逻辑推理，但将推理任务分解为过于简单的步骤有两个重要的缺点。首先，它会阻止今天的方法解决一些看似简单的问题。其次，人类通常无法理解这些简单步骤的一长串序列。该项目探索了一种新的自动推理方法，通过允许更复杂且易于理解的步骤来处理这个问题。半个多世纪以来，有关推理系统的研究一直集中在理论上可以由计算机找到的短论证的存在上，而没有解决如何在实践中实际找到这些论证的问题。该项目研究的新颖推理系统旨在自动查找数学家通常使用的论证，特别是“不失一般性”的论证，这些论证可以有效地自动化。该研究的主要目标是（1）解决现有推理技术难以解决的问题，（2）为我们只有大量论证的问题提供简短的论证，以及（3）从自动推理的结果中学习。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

The key to automating activities that are traditionally performed by humans, such as assembly-line work or organizational tasks, is to break these activities down into numerous simple steps that can be handled easily. While this approach has also been used to automate logical reasoning, breaking reasoning tasks into overly simple steps has two important shortcomings. First, it can prevent today's methods from solving some seemingly easy problems. Second, a long sequence of these simple steps is often impossible to understand for humans. This project explores a novel approach to automated reasoning that deals with this issue by allowing more elaborate, but also understandable, steps.Over half a century, research regarding reasoning systems has centered on the existence of short arguments that could in theory be found by computers, without addressing the issue of how to actually find these arguments in practice. The novel reasoning systems studied in this project aim at automatically finding arguments that are usually used by mathematicians, in particular arguments "without loss of generality," which can be automated efficiently. The main goals of the research are (1) solving problems that are too hard for existing reasoning techniques, (2) producing short arguments for problems for which we only have gigantic arguments, and (3) learning from the results of automated reasoning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.