SHF: Small: WLoS: Without Loss of Satisfaction

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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.