Re: A different definition of MINUS, Part 3

On Dec 21, 4:13 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> Projection, to me, doesn't seem like any sort of union.

OK, in classic relational algebra union can only be applied to the relations with the same header (that is set of attributes). Therefore, when generalizing union to become applicable to any pair of relations one must decide first, what the header the resulting relation should have. D&D assumed it has to also be a union, but I suggest that it can be anything: intersection, difference, or even symmetric difference. However, the last two choices are no good: symmetric difference would make the generalized version of the union incompatible with classic RA union, while difference operation is not symmetric, thus rendering generalized union nonsymmetric as well. Therefore, the only alternative to D&D version of the union is "inner union": it intersects over headers, and unions over tuples. Compare it to join that intersects on tuple level, and unions headers.

Next one may compare D&D <AND>&<OR> based system, with RL join&inner union based one in terms of consistency. Both have arguments in their favor. D&D system honors distributivity, and De Morgan laws. RL honors absorption, so that the subset relation can be generalized to be applicable to any pair of relations. Also RL can express projection as an (inner) union of a relation with an empty relation. First, tuples in both relations (there are none in the second!) are collapsed to the common set of attributes. These are essentially projections. Then we make a union of projections, but keep in mind that the second projection is empty! Received on Mon Dec 22 2008 - 03:04:37 CET