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 $\mathrm{\mathcal{M}}=\left\langle \mathbb{U},\Omega \right\rangle$. By varying Ω and ℳ, constraint databases can model a variety of data models found in practice including traditional relational databases, spatial and spatiotemporal databases, and databases with text fields (strings). More formally, let Ω be a fixed vocabulary consisting of function, predicate, and constant symbols, and let ℛ = {R ₁,  ... , R _ℓ .} be a relational schema, where each relation name R _i is of arity n _i > 0. An Ω-constraint database D with schema ℛ maps each relation R _i  ∈ ℛ to a quantifier-free formula ${\varphi}_{R_i}^{\mathbf{D}}\left({x}_1,...,{x}_{n_i}\right)$...