Formalization and reasoning about spatial semantic integrity constraints

A formalization of spatial semantic integrity constraints is fundamental to assess the data quality of spatial databases. This paper presents a formalization of spatial semantic integrity constraints that provides a uniform specification of constraints used in practice. The formalization extends traditional notions of functional and inclusion dependencies to consider spatial attributes. This enables to impose topological relations between spatial attributes and to impose constraints on numerical attributes that depend on spatial attributes. We also study one of the classical problems of integrity constraints: the satisfiability problem, which consists in checking the existence of a non-empty database that satisfies a given set of constraints. This problem, in the context of spatial databases, rises the qualitative reasoning problems of topological consistency and realizability of spatial constraints. We show that satisfiability is not tractable in general and provide some conditions under which it is. For tractable cases, we also give algorithms that check if a set of constraints is satisfiable. For intractable cases we find conditions under which approximation algorithms can be used.