Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version

• Main Authors: Bezhanishvili, Nick, Ciancia, Vincenzo, Gabelaia, David, Jibladze, Mamuka, Latella, Diego, Massink, Mieke, de Vink, Erik P
• Format: Journal Article
• Language: English
• Published: 09-04-2024
• Subjects: Computer Science - Logic in Computer Science
• DOI: 10.48550/arxiv.2404.06131

In the context of spatial logics and spatial model checking for polyhedral
models -- mathematical basis for visualisations in continuous space -- we
propose a weakening of simplicial bisimilarity. We additionally propose a
corresponding weak notion of $\pm$-bisimilarity on cell-poset models, a
discrete representation of polyhedral models. We show that two points are
weakly simplicial bisimilar iff their repesentations are weakly
$\pm$-bisimilar. The advantage of this weaker notion is that it leads to a
stronger reduction of models than its counterpart that was introduced in our
previous work. This is important, since real-world polyhedral models, such as
those found in domains exploiting mesh processing, typically consist of large
numbers of cells. We also propose SLCS_eta, a weaker version of the Spatial
Logic for Closure Spaces (SLCS) on polyhedral models, and we show that the
proposed bisimilarities enjoy the Hennessy-Milner property: two points are
weakly simplicial bisimilar iff they are logically equivalent for SLCS_eta.
Similarly, two cells are weakly $\pm$-bisimilar iff they are logically
equivalent in the poset-model interpretation of SLCS_eta. This work is
performed in the context of the geometric spatial model checker PolyLogicA and
the polyhedral semantics of SLCS.