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 join (R<AND>B) of given relation R and relational expression B, which is derived from original logical expression b replacing  of logical operators AND, OR, NOT for corresponding relational operators <AND>, <OR>, <NOT>. Then for some tuple T we define a value of attribute A as the relation with the single tuple with the single value of concerned attribute – RELATION<A> {{a}}. The value of attribute marked as NULL meaning the unknown value we define as the 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 definite as equijoin of these attributes represented as relation. The tuple T, which could be presented as Cartesian product over all its attributes, is also definite as a relation R_T. The validity of this tuple T represented as relation R_Tover the original logical expression b means the truth of universal quantifier over the tuples of R_T on expression b, which means equality of join (R_T <AND> B)and R_T  –  (R_T <AND> B)= R_T.