Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta – Extended Version
arxiv(2024)
摘要
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 +/–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 +/–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 +/–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.
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