Constraint Databases

Definition

Constraint databases are a generalization of relational databases aimed to store possibly infinite-sized sets of data by means of a finite representation (constraints) of that data. In general, constraints are expressed by quantifier-free first-order formulas over some fixed vocabulary Ω and are interpreted in some Ω-structure ${\mathcal {M}} =\langle \mathbb{U},{\rm \Omega} \rangle$. By varying Ω and ${\mathcal {M}}$, constraint databases can model a variety of data models found in practice including traditional relational databases, spatial and spatio-temporal databases, and databases with text fields (strings). More formally, let Ω be a fixed vocabulary consisting of function, predicate and constant symbols, and let ${\mathcal {R}} =\{ {R}_{1},{ ...} , {R}_{\ell}.\}$ be a relational schema, where each relation name R _i is of arity n _i > 0. An Ω-constraint database D with schema ${\cal R}$ maps each relation ${R}_{i} \in {\cal R}$ to a quantifier-free formula \({...