Definition
The conjunctive queries are simply the fragment of 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 general form
- ,
with the free variables being called distinguished variables, and the bound variables being called undistinguished variables. are atomic formulae. Conjunctive queries without distinguished variables are called boolean conjunctive queries.
Conjunctive queries can express a large part of queries, which are frequently issued on relational databases. To give an example, imagine a relational database for storing information about students, their address, the courses they visit and their gender. Finding all male students and their addresses who attend a course that is also attended by a female student is expressed by the following conjunctive query:
(student, address) . (student2, course) . attends(student, course) gender(student, 'male') attends(student2, course) gender(student2, 'female') lives(student, address)
Note that since the only entity of interest is the male student and his address, these are the only distinguished variables, while the variables course, student2 are only existentially quantified, i.e. undistinguished.
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