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 = {R1, … , Rℓ.} be a relational schema, where each relation name Ri is of arity ni > 0. An Ω-constraint database D with schema ℛ maps each relation Ri ∈ ℛ to a quantifier-free formula \( {\varphi}_{R_i}^{\mathbf{D}}\left({x}_1,\ldots,{x}_{n_i}\right) \)...
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Geerts, F. (2018). Constraint Databases. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_1268
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