Theory of conjunctive queries

In database theory, a conjunctive query is a restricted form of first-order queries using the logical conjunction operator. 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.

Is a Datalog rule a conjunctive query?

A single Datalog rule can be seen as a conjunctive query [ 1 ].
Optimization and reformulation for various purposes is quite feasible for conjunctive queries, as opposed to general relational calculus/algebra queries.
The equivalence (and indeed the containment) of conjunctive queries is decidable, albeit NP-complete [ 1 ].

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What is a conjunction query in relational calculus?

This entry uses terminology defined in the entry Relational Calculus.
Conjunctive queries are first-order queries of a particular form:

  • {〈 e1
  • …
  • en 〉 ∣ ∃ x1 … xmψ } where ψ is an (equality-free) conjunction of relational atoms
  • i.e., atoms of the form R ( d1 ,…, dk ) (where d1 ,…, dk are variables of constants).
    • In computability theory, many reducibility relations are studied.
    They are motivated by the question: given sets mwe-math-element> and mwe-math-element> of natural numbers, is it possible to effectively convert a method for deciding membership in mwe-math-element> into a method for deciding membership in mwe-math-element>? If the answer to this question is affirmative then mwe-math-element> is said to be reducible to mwe-math-element>.

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