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## Solving NULL issue in queries to a relational database using the operators of relational algebra A.

#### Abstract

Suggest interpreting logical expressions in the relational restriction operator as relational expressions. To be more precise, the relational restriction operator (R WHERE b) over the relation R on some logical expression b can be represented as a join (R<AND>B) of given relation R and relational expression B, which is derived from original logical expression b by replacing of logical operators AND, OR, NOT for corresponding relational operators <AND>, <OR>, <NOT>. Then we define a value of attribute A for some tuple T as the relation with the single tuple and the single value of concerned attribute – RELATION<A> {{a}}. The value of attribute marked as NULL meaning the unknown value is defined as a relation with a head including concerned attribute and the body including all possible values over the type of attribute A – REALTIONAL<A>{…}. The equality values of attributes are defined as equijoin of these attributes represented as relation. The tuple T, which could be presented as Cartesian product over all its attributes, is also defined as a relation RT. The validity of this tuple T represented as a relation RT over the original logical expression b means the truth of universal quantifier over the tuples of RT on expression b, which means equality of join (RT <AND> B) and RT – (RT <AND> B) = RT.

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#### Edition

Proceedings of the Institute for System Programming, vol. 21, 2011, pp. 183-204.

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

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