Mon, Sep 20, 1999
------------------------

- Review of BCNF

- Updating Definition of BCNF given in previous class:

  A relation R is in BCNF iff
  for every nontrivial FD X->Y, X is a superkey.

- Notice the word "nontrivial"

- how BCNF works

- why BCNF works

- how do you know when to stop "splitting"

- Stopping Conditions
  - reach a two-column relation (why?)
  - no FD violations in the splitted relations
    (how do you check this)
       - project the original FDs down to the reduced space
       - pick out only those attributes that matter

- The 3 Desired Properties of Breakups
  - what do they mean

- Properties guaranteed by BCNF
  - first two

- Properties guaranteed by 3NF
  - last two

- What is 3NF?
  - weaker than BCNF

  A relation R is in 3NF iff
  for every nontrivial FD X->Y, X is a superkey
  or Y is part of a key.

- Notice the phrase "Y is part of a key"
  - this excuses some cases that BCNF will not allow

- 3NF is less restrictive than BCNF

- Every BCNF relation is also in 3NF

- 3 example problems solved in class

- MDs: Generalization of FDs
  - written as X->->Y

- 4NF: Addresses a further source of redundancy not addressed by BCNF

- MDs do not obey the same laws as FDs

- In FD-world
	X->Y and X->Z implies X->YZ

- In MD-world
	X->->Y and X->->Z does not imply X->->YZ

- What rules do MDs obey?
	- X->->Y and Y->->Z implies X->->Z
	- X->->Y implies X->->Z where Z is all attributes of R that
          are not among the Y's (why is this true)
	- X->Y implies X->->Y (i.e., every FD is also an MD)

- Definition of 4NF
	- A relation R is in 4NF iff
          for every nontrivial MD X->->Y, X is a superkey

- What does it mean for an MD to be nontrivial?
	- non-intuitive
	- An MD X->->Y is nontrivial iff
		- at least one of the Y's is not among the X's
                       (same as in FD world)
		- X U Y is *not* the set of all attributes

- Why is this catch necessary?
	- otherwise we can have a two-column relation that is not in 4NF

- Bottom line:
	- It is "intuitive" what it means for an FD to be "trivial"
	- It is not so intuitive what it means for an MD to be "trivial"
		- hence the extra clause in the above definition


- 4NF implies BCNF implies 3NF

- Venn Diagram Notation

Wed, Sep 22, 1999
------------------------

- Review of BCNF, 3NF and 4NF definitions

- A small 4NF Problem

- What guarantees do each of the NFs provide?

				               3NF	BCNF	  4NF
--------------------------------------------------------------------------
  Elimination of redundancies due to FDs     Most       Yes       Yes
  Elimination of redundancies due to MDs     No         No        No
  Dependency Preservation: FDs               Yes        Maybe     Maybe
  Dependency Preservation: MDs               Maybe      Maybe     Maybe

- Which normal form to choose?
	- depends on your application
	- is elimination of redundancy important or 
	  is dependency preservation important?

- What exactly is dependency preservation, anyway?
	- examples
	- what's its use: saves time and cost during inserts, updates, etc.

- End of Module 1! (Phew!)

- Module 2 begins

- Introduction to DDL in SQL 

- Introduction to 3 Query Languages

- Return graded homework #2