用数据联合分布推导逻辑抽象，解决符号接地与推理困境
Inference of Abstraction for Grounded Predicate Logic
- 从数据联合分布出发，推导出命题与谓词逻辑的完整联合分布
- 在不依赖贝叶斯网络前提下实现谓词逻辑的可泛化推理
- 为不可判定性、符号接地、爆炸原理等问题提供新解释
人工智能中一个关键未解问题是如何让机器基于具身符号进行有意义的逻辑抽象。本文提出一种概念上全新的方法，将概率推理与谓词符号推理结合。回归贝叶斯网络出现前以完整联合分布为基础的推理时代。我们论证：在命题逻辑中指数规模、在谓词逻辑中无限规模的模型联合分布，应能仅从线性规模的数据联合分布中简单推导得出。研究表明，该过程不仅足以泛化谓词逻辑的逻辑蕴含关系，还能为已知局限如谓词逻辑不可判定性、符号接地问题及爆炸原理提供全新视角。该理论工作的可复现性通过完整证明得以验证。
原文摘要 · Abstract (English)
An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic reasoning and predicative symbolic reasoning over data. We return to the era of reasoning with a full joint distribution before the advent of Bayesian networks. We then discuss that a full joint distribution over models of exponential size in propositional logic and of infinite size in predicate logic should be simply derived from a full joint distribution over data of linear size. We show that the same process is not only enough to generalise the logical consequence relation of predicate logic but also to provide a new perspective to rethink well-known limitations such as the undecidability of predicate logic, the symbol grounding problem and the principle of explosion. The reproducibility of this theoretical work is fully demonstrated by the included proofs.
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