Conjunctive query

In database theory, a conjunctive query is a restricted form of first-order queries. Many first-order queries can be written as conjunctive queries. In particular, a large part of queries issued on relational databases can be expressed in this way. Conjunctive queries also have a number of desirable theoretical properties that larger classes of queries (e.g., the relational algebra queries) do not share.

The conjunctive queries are simply the fragment of (domain independent) first-order logic given by the set of formulae that can be constructed from atomic formulae using conjunction ∧ and existential quantification ∃, but not using disjunction ∨, negation ¬, or universal quantification ∀. Each such formula can be rewritten (efficiently) into an equivalent formula in prenex normal form, thus this form is usually simply assumed.

Thus conjunctive queries are of the following general form:

with the free variables ${\displaystyle x_{1},\ldots ,x_{k}}$ being called distinguished variables, and the bound variables ${\displaystyle x_{k+1},\ldots ,x_{m}}$ being called undistinguished variables. ${\displaystyle A_{1},\ldots ,A_{r}}$ are atomic formulae.

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