Bisimulation for Impure Simplicial Complexes
<|reference_start|>Bisimulation for Impure Simplicial Complexes: As an alternative to Kripke models, simplicial complexes are a versatile semantic primitive on which to interpret epistemic logic. Given a set of vertices, a simplicial complex is a downward closed set of subsets, called simplexes, of the vertex set. A maximal simplex is called a facet. Impure simplicial complexes represent that some agents (processes) are dead. It is known that impure simplicial complexes categorically correspond to so-called partial epistemic (Kripke) models. In this contribution, we define a notion of bisimulation to compare impure simplicial complexes and show that it has the Hennessy-Milner property. These results are for a logical language including atoms that express whether agents are alive or dead. Without these atoms no reasonable standard notion of bisimulation exists, as we amply justify by counterexamples, because such a restricted language is insufficiently expressive.<|reference_end|>
@article{bílková2024bisimulation,
    title={Bisimulation for Impure Simplicial Complexes},
    author={Marta B'ilkov'a, Hans van Ditmarsch, Roman Kuznets, Rojo
  Randrianomentsoa},
    journal={arXiv preprint arXiv:2406.16785},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.16785},
    primaryClass={cs.LO cs.DC}
}