A Topological Semantics of Dialogue: Nerve Structures and Logical Extraction

We introduce a concise, topologically-motivated semantics for finite dialogues by mapping each utterance to an open set in a fixed semantic space, building the corresponding nerve complex of joint satisfiability, and extracting fundamental combinatorial invariants:

@article{santacana2025_2506.00615,
  title={ An Incremental Framework for Topological Dialogue Semantics: Efficient Reasoning in Discrete Spaces },
  author={ Andreu Ballus Santacana },
  journal={arXiv preprint arXiv:2506.00615},
  year={ 2025 }
}