• Corpus ID: 234482811

Geometric Model Checking of Continuous Space

@article{Bezhanishvili2021GeometricMC,
  title={Geometric Model Checking of Continuous Space},
  author={Nick Bezhanishvili and Vincenzo Ciancia and David Gabelaia and Gianluca Grilletti and Diego Latella and Mieke Massink},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.06194}
}
Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as “being near to” or “being surrounded by”. SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images… 
2 Citations

Finite Models for a Spatial Logic with Discrete and Topological Path Operators

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This paper analyses models of a spatial logic with path operators based on the class of neighbourhood spaces, also called pretopological or closure spaces, a generalisation of topological spaces, and shows that the logic admits finite models over quasi-discrete spaces, both with quasi-Discrete and topological paths.

A Spatial Logic for a Simplicial Complex Model

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A spatial logic interpreted on simplicial complexes, topological objects able to represent surfaces and volumes that generalise graphs with higher-order edges that can be verified by a correct and complete model checking algorithm, which is linear to the dimension of the simplicial complex and logical formula.

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