Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917643716395008 |
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| author | Bezhanishvili, Nick Ciancia, Vincenzo Gabelaia, David Jibladze, Mamuka Latella, Diego Massink, Mieke de Vink, Erik P. |
| author_facet | Bezhanishvili, Nick Ciancia, Vincenzo Gabelaia, David Jibladze, Mamuka Latella, Diego Massink, Mieke de Vink, Erik P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version Bezhanishvili, Nick Ciancia, Vincenzo Gabelaia, David Jibladze, Mamuka Latella, Diego Massink, Mieke de Vink, Erik P. Logic in Computer Science 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. |
| title | Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2404.06131 |