A method of spatial reasoning based on qualitative trigonometry
Artificial Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
Current topics in qualitative reasoning
AI Magazine
Composing cardinal direction relations
Artificial Intelligence
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
Combining spatial and temporal logics: expressiveness vs. complexity
Journal of Artificial Intelligence Research
Qualitative spatial and temporal reasoning: efficient algorithms for everyone
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Tools and techniques in qualitative reasoning about space
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
A semi-dynamical approach for solving qualitative spatial constraint satisfaction problems
Theoretical Computer Science
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The main result of this paper is to show that the problem of instantiating a finite and path-consistent constraint network of lines in the Euclidean space is NP-complete. Indeed, we already know that reasoning with lines in the Euclidean space is NP-hard. In order to prove that this problem is NP-complete, we first establish that a particular instance of this problem can be solved by a nondeterministic polynomial-time algorithm, and then we show that solving any finite and path-consistent constraint network of lines in the Euclidean space is at most as difficult as solving that instance.