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.

本文解决了机器如何利用具象符号进行有意义推理的关键问题，提出了一种结合概率推理与谓词符号推理的新方法。研究表明，通过对线性大小数据的全面联合分布，可以有效地推广谓词逻辑的逻辑结果关系，同时提供了重新思考谓词逻辑不可判定性、符号嵌入问题及爆炸原理的新视角。

基于归纳推理的具定语逻辑的抽象推断