关于AI中讨论与论证的第一阶逻辑等式讨论图语义
人工智能
2025-11-14 v4 计算机科学中的逻辑
摘要
我们作出了三项贡献。首先，我们提出了一种针对第一阶逻辑等式的讨论图语义，使我们能够比以往更广泛地处理AI中关于讨论和论证的推理。这解决了当前缺乏能够处理多样化讨论和论证模型的正式推理框架的问题。其次，我们推广了Dung的扩展概念，以处理两个或多个图节点在论证框架中等价的情况。第三，我们将这两个贡献联系起来，表明推广的扩展在提出的讨论图语义中可被第一阶刻画。Dung所有扩展的命题可字符化性是直接的推论。我们进一步表明，所有推广的扩展（可接受性语义）也是可被第一阶刻画的。Dung所有可接受性语义的命题可字符化性是直接的推论。
引用
@article{arxiv.2406.12163,
title = {Discussion Graph Semantics of First-Order Logic with Equality for Reasoning about Discussion and Argumentation},
author = {Ryuta Arisaka},
journal= {arXiv preprint arXiv:2406.12163},
year = {2025}
}
备注
Typos have been corrected. 1. Definition 14: there were two formulas given to 1 \leq k case. One was longer than the other. The longer one has been deleted. 2. Definition 20: corrected a wrong (..) scope in the last conjunct. 3. Theorem 6: the formula after "iff*" contained t_1, ..., t_k, ...., .... They have been corrected. c_1, ..., c_t, ..., 4. Corollary 2: a minor typo corrected