Adding a path connectedness operator to FO+poly (linear)

In the constraint database community, FO+poly and FO+linear have been proposed as foundations for spatial database query languages. One of the strengths of this approach is that these languages are a clean and natural generalization of Codd's relational model to a spatial setting. As a result, rigorous mathematical study of their expressiveness and complexity can be carried out. Along this line, important geometric queries involving connectivity have been shown to be inexpressible in FO+poly and FO+linear. To address this problem, we extend both languages with a parameterized path-connectivity predicate, Pconn. We show that: FO + linear + Pconn and FO+poly+Pconn,3D are closed and have PTIME data complexity. We also examine the expressiveness of FO+poly+Pconn and FO+linear+Pconn and show that parity and transitive closure are expressible in each.

• Type: Journal
• Year: 2002
• Where: ACTA
• Authors: Chris Giannella, Dirk Van Gucht
• Keywords: ACTA 2002, Constraint Database Community, Important Geometric Queries, Spatial Database Query