On Formal IS-A Relationship Definition

April 27, 2010


This posting is an announcement of one more article about Relational Lattice. The later features an analysis of various [partial] order relationships, which may seems too abstract to untrained eye. Let’s assure the reader, that it has practical consequences. In database modeling area the “is-a” relationship is a partial order which coincides with the lattice order “<". Consider the following example (page 12) with the four relations

Animals = [name]
           bear
           sheep
           wolf
;

Carnivores = [name prey]
              bear sheep
              wolf sheep
;

Herbivores = [name  veggi]
              sheep grass
              bear  berries
;

Omnivores = [name veggi prey]
             bear sheep berries
;

Note the “is-a” relationships between Animals and Carnivores, Animals and Herbivores, Carnivores and Omnivores, and finally, between Herbivores and Omnivores. This is four element relational lattice with Omnivores being natural join of Carnivores with Herbivores, while Animals being generalized union of thereof, and the “is-a” relationship is just a lattice order. So, the existence of other partial orders may have significance for modeling too, however, the article in question demonstrates that the order induced by outer union fails to fit this role.

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