用离散空间建模对话语义，实现高效增量推理。
An Incremental Framework for Topological Dialogue Semantics: Efficient Reasoning in Discrete Spaces
- 将话语视为开集，构建对话的单纯复形（神经）结构。
- 提出可证明正确的增量更新算法，支持不一致追踪与蕴含排序。
- 适合研究对话逻辑、形式语义的学者，代码开源可用。
我们提出一种基于有限离散语义空间的可计算、增量式拓扑对话语义框架。基于话语对应开集、其组合关系构成单纯复形（对话神经）的直觉，给出严格基础、可证明正确的增量神经更新算法，并在Wolfram语言中实现参考版本。该框架支持负神经计算（不一致追踪）、蕴含提取及透明的集合论蕴含排序。阐明离散情形下成立的组合性质，提供动机示例，并讨论局限性与更丰富逻辑与范畴扩展的可能性。
原文摘要 · Abstract (English)
We present a tractable, incremental framework for topological dialogue semantics based on finite, discrete semantic spaces. Building on the intuition that utterances correspond to open sets and their combinatorial relations form a simplicial complex (the dialogue nerve), we give a rigorous foundation, a provably correct incremental algorithm for nerve updates, and a reference implementation in the Wolfram Language. The framework supports negative nerve computation (inconsistency tracking), consequence extraction, and a transparent, set-theoretic ranking of entailments. We clarify which combinatorial properties hold in the discrete case, provide motivating examples, and outline limitations and prospects for richer logical and categorical extensions.
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