Reasoning about Betweenness and RCC8 Constraints in Qualitative Conceptual Spaces

Reasoning about Betweenness and RCC8 Constraints in Qualitative Conceptual Spaces

Steven Schockaert, Sanjiang Li

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
Main track. Pages 1963-1969. https://doi.org/10.24963/ijcai.2018/271

Conceptual spaces are a knowledge representation framework in which concepts are represented geometrically, using convex regions. Motivated by the fact that exact conceptual spaces are usually difficult to obtain, we study the problem of spatial reasoning about qualitative abstractions of such representations. In particular, we consider the problem of deciding whether an RCC8 network extended with constraints about betweenness can be realized using bounded and convex regions in a high-dimensional Euclidean space. After showing that this decision problem is PSPACE-hard in general, we introduce an important fragment for which deciding realizability is NP-complete.
Keywords:
Knowledge Representation and Reasoning: Common-Sense Reasoning
Knowledge Representation and Reasoning: Computational Complexity of Reasoning
Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
Knowledge Representation and Reasoning: Qualitative Reasoning