Database Programming

The formal classifications describing the level of database normalization in a data model are called Normal Forms (NF) and the process of doing this is Normalization.

First normal form

First normal form (1NF) lays the groundwork for an organised database design:

Ensure that each table has a primary key: minimal set of attributes which can uniquely identify a record.

Eliminate repeating groups (categories of data which would seem to be required a different number of times on different records) by defining keyed and non-keyed attributes appropriately.

Atomicity: Each attribute must contain a single value, not a set of values.

'First normal form' depends on functional dependency formula f(x)=y. For every value of x there is value for y.

Second normal form

Second normal form (2NF) If a table has a composite key, all attributes must be related to the whole key:

The database must meet all the requirements of the first normal form.

The relational schema should not have any partial functional dependency i.e. No proper subset of the primary key should derive a functional dependency belonging to the same schema. For example, consider functional dependencies FD:{AB->C, A->D, C->D} here AB is the primary key, as A->D this relational schema is not in 2NF.

Third normal form

Third normal form (3NF) requires that data stored in a table be dependent only on the primary key, and not on any other field in the table.

The database must meet all the requirements of the first and second normal form.

All fields must be directly dependent on the primary key field. Any field which is dependent on a non-key field which is in turn dependent on the Primary Key (ie a transitive dependency) is moved out to a separate database table.

4 FOURTH AND FIFTH NORMAL FORMS
Fourth [5] and fifth [6] normal forms deal with multi-valued facts. The multi-valued fact may correspond to a many-to-many relationship,

4.1 Fourth Normal Form
Under fourth normal form, a record type should not contain two or more independent multi-valued facts about an entity. In addition, the record must satisfy third normal form.

Fifth normal form deals with cases where information can be reconstructed from smaller pieces of information that can be maintained with less redundancy. Second, third, and fourth normal forms also serve this purpose, but fifth normal form generalizes to cases not covered by the others.

Boyce-Codd normal form

Boyce-Codd normal form (or BCNF) requires that there be no non-trivial functional dependencies of attributes on something other than a superset of a candidate key (called a superkey).

"The present list of 19 rules of inference constitutes a COMPLETE system of truth-functional logic, in the sense that it permits the construction of a formal proof of validity for ANY valid truth-functional argument." (FN1)

The first nine rules of the list are rules of inference that "correspond to elementary argument forms whose validity is easily established by truth tables." (Id, page 351). The remaining ten rules are the Rules of Replacement, "which permits us to infer from any statement the result of replacing any component of that statement by any other statement logically equivalent to the component replaced." (Id, page 359).

Here are the 19 Rules of Inference:

1. Modus Ponens (M.P.)

p q

p

q 2.Modus Tollens (M.T.)

p q

~q

~p 3.Hypothetical Syllogism (H.S.)p q

q r

p r 4.Disjunctive Syllogism (D.S.)p v q

~ p

q 5. Constructive Dilemma (C.D.)(p q) . (r s)

p v r

q v s 6. Absorption (Abs.)p q

p (p. q)

7. Simplification (Simp.)p . q

p 8. Conjunction (Conj.)p

q

p . q 9. Addition (Add.)p

p v q

Any of the following logically equivalent expressions can replace each other wherever they occur:

10.De Morgan's Theorem (De M.) ~(p . q) (~p v ~q)

~(p v q) (~p . ~q) 11. Commutation (Com.)(p v q) (q v p)

(p . q) (q . p) 12. Association (Assoc.)[p v (q v r)] [(p v q) v r]

[p . (q . r)] [(p . q) . r] 13.Distribution (Dist) [p . (q v r)] [(p . q) v (p . r)]

[p v (q . r)] [(p v q) . (p v r)] 14.Double Negation (D.N.)p ~ ~p 15. Transposition (Trans.)(p q) (~q ~p) 16. Material Implication (M. Imp.)(p q) (~p v q) 17. Material Equivalence (M. Equiv.)(p q) [(p q) . (q p)]

(p q) [(p . q) v (~p . ~q)] 18. Exportation (Exp.)[(p . q) r] [p (q r)] 19. Tautology (Taut.) p (p v p)

p (p . p)

FN1: Introduction to Logic, Irving M. Copi and Carl Cohen, Prentice Hall, Eleventh Edition, 2001, page 361. The book contains the following footnote after this paragraph: "A method of proving this kind of completeness for a set of rules of inference can be found in I. M. Copi, Symbolic Logic, 5th Edition. (New York: Macmillian, 1979), chap 8, See also John A. Winnie, "The Completeness of Copi's System of Natural Deduction," Notre Dame Journal of Formal Logic 11 (July 1970), 379-382."

Class diagram is UML diagram describing static structure of a system on the (lowest) level of classifiers (classes, interfaces, etc.). It shows system's classifiers, their attributes, and the relationships between classifiers.

The following nodes and edges are typically drawn in a UML Class diagram:

• Class
• Interface
• Interface Realization
• Required Interface
• Association
• Generalization
• Dependency

"An entity is a person, place, event, or thing about which data is collected...An instance is an occurence of an entity." - Systems Analysis & Design (4th) - Dennis

An example of this would be STUDENT as the entity while JACK SMITH is an instance of that entity.

If an entity is an individual "person, place, event, or thing about which data is collected", then an entity is an instance. Linguistically, entity is just another word for a single thing ("The existence of a thing as contrasted with its attributes.", Merriam-Webster's On-line Dictionary). Entities that have the same attributes are grouped in what are best called entity classes (it doesn't make sense to refer to a collection of entities as an entity). Entity and entity class are data modeling terms. The corresponding object modeling terms are object and class, albeit that a class typically has operations, which are foreign to an entity class.

A Relational Database Management System (RDBMS) is a Database Management System (DBMS) that is based on the relational model as introduced by E. F. Codd. Most popular commercial and open source databases currently in use are based on the relational model.A short definition of an RDBMS may be a DBMS in which data is stored in the form of tables and the relationship among the data is also stored in the form of tables.

Network topology is the physical interconnections of the elements (links, nodes, etc.) of a computer network. A local area network (LAN) is one example of a network that exhibits both a physical topology and a logical topology. Any given node in the LAN has one or more links to one or more other nodes in the network and the mapping of these links and nodes in a graph results in a geometrical shape that may be used to describe the physical topology of the network. Likewise, the mapping of the data flows between the nodes in the network determines the logical topology of the network. The physical and logical topologies may or may not be identical in any particular network.

Hope this helps!

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