1. Normal forms - 1NF, 2NF and 3NF
(under the assumption of relations with just one candidate key)

2. Aim to familiarise with the concept of a normal form
simplifying assumption (SA)
every relation has one candidate key only, which is, therefore, the primary key

3. Generalities normal forms
expressing FD constraints through choosing the structure of relations (structure  the component attributes)
3NF  2NF  1NF
transforming a relation into a higher normal form
(vertical) decomposition - projection
non-loss decomposition

4. 1NF
a relation is in 1NF if and only if all the domains of its attributes contain only scalar values

5. Relation in 1NF : Students-Info

6. 1NF - update anomalies insert: exercise delete: exercise
modify (update)
suppose “Databases” changes to “3sem” and “1.5cu”
the modification must be performed in more than one tuple; it implies a search;
this structure (1NF) does not enforce consistent data; i.e. inconsistencies can be generated (e.g. by mistake)
(implementation aspect) an update (involving a search) can be expressed by means of a single SQL statement, but
the search still has to be performed
an incorrect statement can generate inconsistencies

7. FD diagram for 1NF
not all the determinants are the primary key

8. 2NF
A relation (with just one CK) is in 2NF if and only if it is in 1NF and every non-key attribute is irreducibly dependent on the primary key
“Students-Info” is not 2NF;
it can be decomposed into a set of relations in 2NF
the equivalence must be preserved

9. Non-loss decomposition
a decomposition of R into its projections R1, …, Rn is non-loss if and only if the natural join of R1, …, Rn results in the initial R

10. Non-loss decomposition

11. Activity
consider different relations and experiment with different decompositions - identify which ones are lossy and which ones are non-loss

12. Heath’s theorem
Suppose A, B and C are sets of attributes of a relation R, such that
AB and
heading(R) = A  B  C
then
R = {A, B} JOIN {A, C}

13. Pragmatic principles
when you apply Heath’s theorem look for a maximum set of attributes B
this will minimise the number of tables in the database
try to maintain a one to one correspondence with real life entities

14. 2NF - update anomalies consider the relation “Module” insert delete
insert that a “3sem” module is worth “1.5cu”
delete
exercise
modify (update)

15. FD for 2NF
transitive dependency

16. 3NF
A relation (with just one CK) is in 3NF if and only if it is in 2NF and every non-key attribute is non-transitively dependent on primary key
alternatively …
if there are no FDs between non-key attributes

17. Modules - decomposed (non-loss)

18. Concluding remarks
all definitions given were for relations with just 1CK
any relation can be decomposed into a set of 3NF relations
3NF is always achievable
are all non-loss decompositions equivalent?
what happens in the case of relations with more than 1CK?