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

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 , EXPTIMEcomplete over polyhedra in R3 , and NP-complete over regular closed sets in R3 .

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Roman Kontchakov, Yavor Nenov, Ian Pratt-Hartmann, Michael Zakharyaschev
• Keywords: Boolean Operations, CORR 2011, Education, Low-dimensional Euclidean Spaces, Regular Closed Sets