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Towards Concise, Machine-Discovered Proofs of Godel's Two Incompleteness Theorems

机译:走向简洁的,机器发现的戈德尔的两个不完整定理证明

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There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we present MATR, a new framework for automated theorem proving explicitly designed to easily adapt to unusual logics or integrate new reasoning processes. MATR is formalism-agnostic, highly modular, and programmer-friendly. We explain the high-level design of MATR as well as some details of its implementation. To demonstrate MATR's utility, we then describe a formalized metalogic suitable for proofs of Godel's Incompleteness Theorems, and report on our progress using our metalogic in MATR to semi-autonomously generate proofs of both the First and Second Incompleteness Theorems.
机译:越来越兴趣在AI中应用最近的AI进程来实现自动推理,因为它可以在一流的,二阶或甚至元逻辑上推理形式主义来提供有用的启发式。 为了促进这项研究,我们呈现了MIGR,这是一种新的自动定理的新框架,明确地设计用于轻松适应异常逻辑或集成新的推理过程。 MIRG是形式主义 - 不可知论者,高度模块化和程序员友好。 我们解释了MIGR的高级设计以及其实现的一些细节。 为了展示MOTT的实用程序,我们描述了适合戈德尔不完整定理证明的正式的Metalogic,以及使用我们的Metalogic在第一个和第二个不完整定理的半自动产生证据的情况下报告我们的进展。

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