Position Spaces and Graphs
In this paper, we introduce position graphs, a graph-based reasoning framework based on the formalization of position spaces. This framework utilizes two strict partial orders, representing horizontal and vertical alignment and precedence, to model the relative positions of discrete tokens. Unlike general qualitative spatial calculi, position graphs are constrained by a chain condition and compatibility requirements that focus on rows and columns. We provide a comprehensive theoretical analysis of this representation, beginning with a characterization of graph consistency. Conditions to ensure the consistency of position graphs are established. Furthermore, we investigate the computationa...
| Authors | Rita-Nathalia Assaf, Tom Davot, Frédéric Lardeux et al. |
|---|---|
| Primary category | cs.AI |
| Published | 24 June 2026 |
| Last updated at source | 24 June 2026 |
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