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Chapter 5 Relational Model Concepts. Dr. Bernard Chen Ph.D. University of Central Arkansas Fall 2008. Relational Model Concepts. A Relation is a mathematical concept based on the ideas of sets The model was first proposed by Dr. E.F. Codd of IBM Research in 1970 in the following paper: - PowerPoint PPT Presentation
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Chapter 5 Relational Model Concepts
Dr. Bernard Chen Ph.D.University of Central Arkansas
Fall 2008
Relational Model Concepts A Relation is a mathematical concept based on
the ideas of sets
The model was first proposed by Dr. E.F. Codd of IBM Research in 1970 in the following paper: "A Relational Model for Large Shared Data
Banks," Communications of the ACM, June 1970
The above paper caused a major revolution in the field of database management and earned Dr. Codd the coveted ACM Turing Award
Outline
Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations
Relational Model Constrains and Relational Database Schemas
Update Operations, Transactions, and Dealing with Constrain Violations
Relational Model Concepts The relational model represents the
database as a collection of relations
Each relation resembles a table of values
When a relation is thought of as a table of values, each row in the table represents a collection of related data values
Formal Terminology A row is called a tuple A column header is called an
attribute The table is called relation
Domain A Domain D is a set of atomic values.
Atomic means that each value in the domain is indivisible as far as the relational model is concerned
It means that if we separate an atomic value, the value itself become meaningless, for example:
SSN Local_phone_number Names Employee_ages
Relation Schema Relation Schema R, denoted by R(A1, A2,…, An), is
made up of relation name R and a list of attributes A1, A2, …,An
Each attribute Ai is the name of a role played by some domain D in the relation schema R.
D is called the domain of Ai and is denoted by dom(Ai)
R is called the name of the relation
The degree of a relation is the number of attributes n of its relation schema
Formal Definitions Formally,
Given R(A1, A2, .........., An) r(R) dom (A1) X dom (A2) X ....X
dom(An)
R(A1, A2, …, An) is the schema of the relation
R is the name of the relation
A1, A2, …, An are the attributes of the relation
Formal Definitions Let R(A1, A2) be a relation schema:
Let dom(A1) = {0,1} Let dom(A2) = {a,b,c}
Then: dom(A1) X dom(A2) is all possible combinations:{<0,a> , <0,b> , <0,c>, <1,a>, <1,b>, <1,c> }
The relation state r(R) dom(A1) X dom(A2)
Definition Summary
Informal Terms Formal Terms
Table Relation
Column Header Attribute
All possible Column Values
Domain
Row Tuple
Table Definition Schema of a Relation
Populated Table State of the Relation
Outline
Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations
Relational Model Constrains and Relational Database Schemas
Update Operations, Transactions, and Dealing with Constrain Violations
Ordering
Ordering of Tuples is a Relation a relation is defined as a set of tuples. Mathematically, elements of a set have
NO order among them The ordering indicates first, second, ith,
and last records in the file Hence, the following two relations are
identical
Identical Relations
Values in the Tuples Each value in a tuple is an atomic value
Hence, composite and multi-valued attributes are not allowed
This model is sometimes called the flat relational model
Much of the theory behind the relational model was developed with this assumption, which is called first normal form assumption
Null in tuples
An important concept is that if NULL values, which are used to represent the values of attributes that may be unknown or may not apply to a tuple
Relational Model Notation
An attribute A can be qualified with the relation name R to which it belongs by using the dot notation R.A
For example, STUDENT.Name or STUDENT.Age
Relational Model NotationWe refer to component values of a tuple t by:
t[Ai] or t.Ai This is the value vi of attribute Ai for tuple t Both t[Ai, Aj, Ak] or t.(Ai, Aj, Ak) refers to a list of
attributes from R
For example: consider a tuple t=< “Barbara Benson”, “533-69-1238”, “839-8461”, “7384 Fontana Lane”, NULL, 19, 3.25> from the STUDENT relation in Figure 5.1
We have t.name=< “Barbara Benson”,> t. (Ssn, Gpa, Age) = <“533-69-
1238”,3.25,19>
Outline
Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations
Relational Model Constrains and Relational Database Schemas
Update Operations, Transactions, and Dealing with Constrain Violations
Domain Constrains Each attribute A must be an atomic
value from the dom(A)
The data types associated with domains typically include standard numeric data type for integers, real numbers, Characters, Booleans, fix-length strings, time, date, money or some special data types
Key Constrains A relation is defined as a set of tuples By definition, all elements of a set are
distinct This means that no two tuples can have
the same combination of values for all their attributes
Superkey: a set of attributes that no two distinct tuples in any state r of R have the same value
Every relation has at least one default superkey – the set of all its attributes
Key Constrains
A superkey can have redundant attributes, so a more useful concept is that of a KEY which has no redundancy
Key satisfied two constrains: Two distinct tuple in any state of the
relation cannot have identical values for the attributes in the key
It is a minimal superkey
Key Constrains For example, consider STUDENT
relation The attribute set {SSN} is a key of
STUDENT because no two student can have the same value for SSN
Any set of attributes that includes SSN – for example {SSN, Name, Age} – is a superkey
Key Constrains In general, a relation schema may have
more than one key, in this case, each of the key is called a candidate key
Example: Consider the CAR relation schema: CAR(State, Reg#, SerialNo, Make, Model, Year) CAR has two keys:
Key1 = {State, Reg#} Key2 = {SerialNo}
Both are also superkeys of CAR {SerialNo, Make} is a superkey but not a key.
Key Constrains
If a relation has several candidate keys, one is chosen arbitrarily to be the primary key.
Example: Consider the CAR relation schema: CAR(State, Reg#, SerialNo, Make, Model, Year) We chose SerialNo as the primary key
The primary key value is used to uniquely identify each tuple in a relation
Provides the tuple identity
Also used to reference the tuple from another tuple General rule: Choose as primary key the smallest of the candidate
keys (in terms of size) Not always applicable – choice is sometimes subjective
CAR table with two candidate keys – LicenseNumber chosen as Primary Key
Key Constrains and Constrains on NULL values
Another constraint on attributes specifies whether NULL value are or are not permitted
For example, if every STUDENT tuple must have a valid, non-NULL value for the Name attribute, then Name of STUDENT is constrained to be NOT NULL
Relational Database Schema Relational Database Schema:
A set S of relation schemas that belong to the same database.
S is the name of the whole database schema S = {R1, R2, ..., Rn} R1, R2, …, Rn are the names of the individual
relation schemas within the database S Following slide shows a COMPANY database
schema with 6 relation schemas
COMPANY Database Schema
Entity Integrity Entity Integrity:
The primary key attributes PK of each relation schema R in S cannot have null values in any tuple of r(R).
This is because primary key values are used to identify the individual tuples.
t[PK] null for any tuple t in r(R) If PK has several attributes, null is not allowed in any of
these attributes Note: Other attributes of R may be constrained
to disallow null values, even though they are not members of the primary key.
Referential Integrity Constraint Referential Integrity Constraint is specified
between two relations and is used to maintain the consistency among tuples in the two relations
Informally define the constrain: a tuple in one relation must refer to an existing tuple in that relation
For example, the Dno in EMPLOYEE gives the department number for which each employee works, this number must match the Dnumber value in DEPARTMENT
Referential Integrity Constraint Tuples in the referencing
relation R1 have attributes FK (called foreign key attributes) that reference the primary key attributes PK of the referenced relation R2. A tuple t1 in R1 is said to reference a
tuple t2 in R2 if t1[FK] = t2[PK].
Displaying a relational database schema and its constraints Each relation schema can be displayed as a row of attribute
names The name of the relation is written above the attribute
names The primary key attribute (or attributes) will be underlined
A foreign key (referential integrity) constraints is displayed as a directed arc (arrow) from the foreign key attributes to the referenced table
Can also point the the primary key of the referenced relation for clarity
Next slide shows the COMPANY relational schema diagram
Referential Integrity Constraints for COMPANY database
Other Types of Constraints Semantic Integrity Constraints:
based on application semantics and cannot be expressed by the model per se
Example: “the max. no. of hours per employee for all projects he or she works on is 56 hrs per week”
A constraint specification language may have to be used to express these
Outline
Relational Model Concepts Domains, Attributes, and Relations Characteristics of Relations
Relational Model Constrains and Relational Database Schemas
Update Operations, Transactions, and Dealing with Constrain Violations
Modification and Updates In this section, we concentrate on the
database Updates and Modification
There are threee basic operation: Insert, Delete and Modify Insert is used to insert a new tuple or tuples
in a relation Delete is used to delete tuples Update (or Modify) is used to change the
values of some attributes
Modification and Updates Insert: insert new element with specify
all related attributes
Delete: delete an element by giving Relation name and key of the tuple
Modify: modify a value by giving a relation name, Key of the target tuple and attribute to modify
Possible violations for each operation INSERT may violate any of the constraints:
Domain constraint: if one of the attribute values provided for the new tuple is
not of the specified attribute domain Key constraint:
if the value of a key attribute in the new tuple already exists in another tuple in the relation
Referential integrity: if a foreign key value in the new tuple references a primary
key value that does not exist in the referenced relation Entity integrity:
if the primary key value is null in the new tuple
Insert Example Insert <‘Cecilia’, ‘F’, ‘Kolonsky’, NULL, ‘1960-
04-05’, ‘6357 Windy lane,Kate,TX’, F, 28000, NULL, 4> into EMPLOYEE
Insert < ‘Cecilia’, ‘F’, ‘Kolonsky’, 999887777, ‘1960-04-05’, ‘6357 Windy lane,Kate,TX’, F, 28000, NULL, 4 >
Cecilia’, ‘F’, ‘Kolonsky’, 667788999, ‘1960-04-05’, ‘6357 Windy lane,Kate,TX’, F, 28000, NULL, 7>
Possible violations for each operation DELETE may violate only referential integrity:
If the primary key value of the tuple being deleted is referenced from other tuples in the database
Can be remedied by several actions: RESTRICT, CASCADE, SET NULL
RESTRICT option: reject the deletion CASCADE option: propagate the new primary key value into
the foreign keys of the referencing tuples SET NULL option: set the foreign keys of the referencing
tuples to NULL
One of the above options must be specified during database design for each foreign key constraint
Delete Example Delete the EMPLOYEE tuple with
Ssn=‘99988777’
Delete the EMPLOYEE tuple with Ssn=‘333445555’
Delete the EORKS_ON tuple eith Essn=‘999887777’ and Pno=10
Possible violations for each operation UPDATE may violate domain constraint and NOT NULL
constraint on an attribute being modified
Any of the other constraints may also be violated, depending on the attribute being updated:
Updating the primary key (PK): Similar to a DELETE followed by an INSERT Need to specify similar options to DELETE
Updating a foreign key (FK): May violate referential integrity
Updating an ordinary attribute (neither PK nor FK): Can only violate domain constraints
Update Example Update the salary of EMPLOYEE tuple with
Ssn=‘999887777’ to 2800
Update the Dno of the EMPLOYEE tuple with Ssn=‘999887777’ to 1
Update the Dno of the EMPLOYEE tuple with Ssn=‘999887777’ to 7
Update the Ssn of the EMPLOYEE tuple with Ssn=‘999887777’ to ‘987654321’