Database Systems: A Practical Approach to Design, by Thomas M. Connolly

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By Thomas M. Connolly

This booklet takes a clean, pragmatic method of database platforms. With a powerful layout concentration and utilizing life like case stories all through, readers can grasp an obtainable, step by step technique, observe this to layout and construct functions, and achieve a superb figuring out of the problems interested in construction the structures.

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By h2 , [Child] in G is mapped to [Child:Paul] in H, by h1 it is mapped to [Child]. The relation (act) is mapped to the appropriate relation (playWith). The other nodes have the same image by both homomorphisms: [Toy] and [Car] are mapped to [FireTruck], the two relations (on) are mapped to the sole relation (on) in H, and each remaining node is mapped to the node with same label in H. 32 2 Basic Conceptual Graphs h1 h2 Child Child:Paul 1 Child 1 act 2 Toy 1 attr 2 Color:red playWith playWith 2 Fig.

3 Elementary Specialization Operations The elementary specialization operations defined in this section are inverse (up to an abuse of language explained hereafter) operations of the elementary generalization operation defined previously. Besides the copy operation, there are three unary operations and one binary operation. 17 (Elementary specialization operations). The five elementary specialization operations are: • Copy (already defined as a generalization operation). • Relation simplify. Given a BG G, and two twin relations r and r (relation with the same type and the same list of neighbors), relationSimpli f y(G, r ) is the BG obtained from G by deleting r .

For this we use the following property. 8. Let G be any BG and H be an irredundant BG. If G is hom-equivalent to H, then G has a subBG isomorphic to H. Proof. If G and H are hom-equivalent, there is a homomorphism, say π , from H to G and a homomorphism, say π , from G to H. Now consider the homomorphism π ◦ π from H to H. 7). Let G = π (H). Let us show that π is an isomorphism from H to G . π is surjective by definition of G , and π is injective since π ◦ π is injective. Thus π is a bijective homomorphism from H to G .

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