# Positive Relational Algebra

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**DOI:**https://doi.org/10.1007/978-1-4899-7993-3_1251-2

## Synonyms

## Definition

Positive relational algebra is the fragment of relational algebra which excludes the difference operator. Relational algebra queries are expressions defining mappings from database instances of an input database schema to an output relation. In particular a positive relational algebra query over a database schema τ is one of the following expressions, each one with an associated set of attributes:

A constant relation over a set of attributes

*U*is a positive relational algebra query with associated set of attributes*U*.If

*R*(*U*) is a relation schema in τ, the relation symbol*R*is a positive relational algebra query with associated set of attributes*U*.-
If
*Q*and*Q*′ are positive relational algebra queries with sets of attributes*U*and*U*′, respectively, the following are positive relational algebra queries:The

*selection σ*_{A=B}(*Q*) or*σ*_{A=c}(*Q*), with set of attributes*U*, where*A*and*B*are attributes in*U*, and*c*is a constant valueThe

*projection*π_{X}...

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## Recommended Reading

- 1.Abiteboul S, Hull R, Vianu V. Foundations of databases. Reading: Addison-Wesley; 1995.Google Scholar

## Copyright information

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