# A different definition of MINUS, part 4

From: paul c <toledobythesea_at_oohay.ac>

Date: Fri, 26 Dec 2008 11:37:37 -0800

Message-ID: <Zma5l.8523$fc3.1985_at_newsfe02.iad>

Parts one, two and three have various mis-steps and confusions. Let me start again emphasizing what I think was McGoveran's paramount point - the desire for logical data independence. I interpret the meaning of this in an algebra to be that substituting some non-logical aspect of an implementation for another will not require any logical aspects to be removed, ie., any true statements to be falsified. Base and virtual relvars are non-logical aspects in that there is no notion of them in the algebra or calculus. In Codd's logic, ie. his algebra and calculus, they are no different than colours, for example it does not matter in the D&D A-algebra whether a relation is 'red' or 'green'. This does not mean that an implementation cannot be logical, only that if its results are to be validated logically, it must define all the concepts involved in those results in logical, eg., algebraic, terms.

Date: Fri, 26 Dec 2008 11:37:37 -0800

Message-ID: <Zma5l.8523$fc3.1985_at_newsfe02.iad>

Parts one, two and three have various mis-steps and confusions. Let me start again emphasizing what I think was McGoveran's paramount point - the desire for logical data independence. I interpret the meaning of this in an algebra to be that substituting some non-logical aspect of an implementation for another will not require any logical aspects to be removed, ie., any true statements to be falsified. Base and virtual relvars are non-logical aspects in that there is no notion of them in the algebra or calculus. In Codd's logic, ie. his algebra and calculus, they are no different than colours, for example it does not matter in the D&D A-algebra whether a relation is 'red' or 'green'. This does not mean that an implementation cannot be logical, only that if its results are to be validated logically, it must define all the concepts involved in those results in logical, eg., algebraic, terms.

Suppose R is virtual, A and B are base and R is defined as A JOIN B:

Now, make R base and A and B virtual (logical independence should allow this):

A = R{HA} is true.

B = R{HB} is true.

R MINUS D is semantically equivalent to:

((R{HR1} <NXOR> R{HR2}) <AND> (<NOT> D)){HR}

where (ie., 'it is required that') HR is the heading of R
and

HR1 union HR2 = HR,