On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces

@inproceedings{Kontchakov2011OnTD,
  title={On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces},
  author={Roman Kontchakov and Yavor Nenov and Ian Pratt-Hartmann and Michael Zakharyaschev},
  booktitle={IJCAI},
  year={2011}
}
We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates, as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of the space and on the type of regions considered. For example, the logic with the interior-connectedness predicate (and without contact) is undecidable over polygons or regular closed sets in R2… 
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