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Fundamentals of
Database Systems
Chapter 5
The Relational Data Model
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Chapter Outline
 Relational Model Concepts
 Relational Model Constraints and Relational
Database Schemas
 Update Operations and Dealing with
Constraint Violations
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Relational Model Concepts
 Basis of the model
 The relational Model of Data is based on the
concept of a Relation
» The strength of the relational approach to data
management comes from the formal foundation provided
by the theory of relations
 We review the essentials of the formal relational
model in this chapter
 In practice, there is a standard model based on SQL
– this is described in Chapters 8 and 9
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Relational Model Concepts (cont.)
 A Relation is a mathematical concept based
on the ideas of sets
 The model was first proposed by Dr. E.F.
Codd of IBM in 1970
» "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
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Relational Model Concepts (cont.)
 Informal Definitions
 RELATION: A table of values
» A relation may be thought of as a set of rows
» A relation may alternately be though of as a set
of columns
» Each row of the relation may be given an
identifier
» Each column typically is called by its column
name or column header or attribute name
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Relational Model Concepts (cont.)
 Formal Definitions
 The Schema of a Relation R (A1, A2, .....An)
» Relation schema R is defined over attributes A1,
A2, .....An
» Each attribute Ai is the name of a role played by
some domain D in the relation schema R
» e.g., A relation schema
STUDENT(Name, SSN, HomePhone, Address,
OfficePhone, Age, GPA)
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Relational Model Concepts (cont.)
 A relation r(R) is a subset of the Cartesian
product of the domains that define R
» r(R)  (dom (A1)  dom (A2)  ....  dom(An))
» e.g., Let S1 = {0,1}, S2 = {a,b,c}
r(R) = {<0, a>, <0, b>, <1, c>}
 A relation may be regarded as a set of tuples
(rows)
» r = {t1, t2, . . ., tm}.
» A tuple is an ordered set of values
t = <v1, v2, . . ., vn>
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Relational Model Concepts (cont.)
 R is also called the intension of a relation
 r is also called the extension of a relation
 The degree of a relation is the number of
attributes n of its relation schema
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Relational Model Concepts (cont.)
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Relational Model Concepts (cont.)
 Definition summary
Informal Terms
Formal Terms
Table
Relation
Column
Attribute/Domain
Row
Tuple
Values in a column Domain
Table Definition
Schema of Relation
Populated Table
Extension
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Characteristics of Relations
 Ordering of tuples in a relation r(R)
 The tuples are not considered to be ordered,
even though they appear to be in the tabular
form
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Characteristics of Relations (cont.)
 Ordering of attributes in a relation schema R
 We will consider the attributes in R(A1, A2, ...,
An)
and the values in t=<v1, v2, ..., vn> to be ordered
 A more general alternative definition of relation
does not require this ordering
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Characteristics of Relations (cont.)
 Values in a tuple
 All values are considered atomic (indivisible)
 A special null value is used to represent
values that are unknown or inapplicable to
certain tuples
» e.g., OfficePhone for some students
 We refer to component values of a tuple t by
t[Ai] = vi (the value of attribute Ai for tuple t)
 Similarly, t[Au, Av, ..., Aw] refers to the
subtuple of t containing the values of
attributes Au, Av, ..., Aw, respectively
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Relational Integrity Constraints
 Constraints are conditions that must hold
on all valid relation instances
 Three main types of constraints:
 Key constraints
 Entity integrity constraints
 Referential integrity constraints
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Relational Integrity Constraints (cont.)
 Key Constraints
 Superkey of R
» A set of attributes SK of R such that no two
tuples in any valid relation instance r(R) will
have the same value for SK, i.e., for any distinct
tuples t1 and t2 in r(R), t1[SK] <> t2[SK]
 Key of R
» A minimal superkey
» A superkey K such that removal of any attribute
from K results in a set of attributes that is not a
superkey
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Relational Integrity Constraints (cont.)
» If a relation has several candidate keys, one is
chosen arbitrarily to be the primary key
» The primary key attributes are underlined
» e.g,
CAR(State, Reg#, SerialNo, Make, Model, Year)
two keys, Key1 = {State, Reg#},
Key2 = {SerialNo}
{SerialNo, Make} is a superkey but not a key
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Relational Integrity Constraints (cont.)
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Relational Integrity Constraints (cont.)
 Entity Integrity
 Relational database schema
» A set S of relation schemas that belong to the
same database
» S is the name of the database, S = {R1, R2, ..., Rn}
 A relational database state DB of S
» A set of relation states DB = {r1, r2, . . ., rm}
such that each ri is a state of Ri
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Relational Integrity Constraints (cont.)
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Relational Integrity Constraints (cont.)
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Relational Integrity Constraints (cont.)
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Relational Integrity Constraints (cont.)
 Entity Integrity
» The primary key attributes PK of each relation
schema R in S cannot have null values in any
tuple of r(R), i.e.,
t[PK] <> null for any tuple t in r(R)
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Relational Integrity Constraints (cont.)
 Referential Integrity
 A constraint used to specify a relationship
among tuples in two relations: the referencing
relation and the referenced relation
 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
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Relational Integrity Constraints (cont.)
 A tuple t1 in R1 is said to reference a tuple t2
in R2 if t1[FK] = t2[PK]
 A referential integrity constraint can be
displayed in a relational database schema as a
directed arc from R1.FK to R2
 A foreign key can refer to its own relation
» e.g., the attribute SUPERSSN in EMPLOYEE
refers to the supervisor of an employee
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Relational Integrity Constraints (cont.)
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Relational Integrity Constraints (cont.)
 Other types of constraints
 Semantic integrity constraints
» e.g., the salary of an employee should not exceed
the salary of the employee’s supervisor
 Transition constraints
» Used to deal with state changes in the database
» e.g., the salary of an employee can only increase
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Update Operations on Relations
 Three basic update operations
 INSERT a tuple
 DELETE a tuple
 MODIFY a tuple
 Integrity constraints should not be
violated by the update operations
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Update Operations on Relations (cont.)
 Insert can violate any of the four types of
constraints
» Insert <‘Cecilia’, ‘F’, ‘Kolonsky’, null, ‘1960-0405’, ‘6357 Windy Lane, Katy, TX’, F, 28000, null,
4> into EMPLOYEE
– violates the entity integrity constraint (null for the
primary key SSN)
» Insert <‘Alicia’, ‘J’, ‘Zelaya’, ‘999887777’,
‘1960-04-05’, ‘6357 Windy Lane, Katy, TX’, F,
28000, ‘987654321’, 4> into EMPLOYEE
– violates the key constraint because ‘999887777’ exists
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Update Operations on Relations (cont.)
 The Delete operation can violate only
referential integrity, if the tuple being deleted
is referenced by the foreign keys from other
tuples in the database
» Delete the EMPLOYEE tuple with SSN =
‘999887777’
– is not acceptable, because tuples in WORKS_ON
refer to this tuple
» Delete the EMPLOYEE tuple with SSN =
‘333445555’
– result in even worse referential integrity violations
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Update Operations on Relations (cont.)
 Updating an attribute that is neither a primary
key nor a foreign key usually causes no
problems
 Modifying a primary key value is similar to
deleting one tuple and inserting another in its
place
 If a foreign key attribute is modified, the
DBMS must make sure that the new value
refers to an existing tuple in the referenced
relation (or is null)
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Chapter Summary
 Presented relational model concepts
 Definitions
 Characteristics of relations
 Discussed relational model constraints and
relational database schemas




Domain constraints’
Key constraints
Entity integrity
Referential integrity
 Described the relational update operations and
dealing with constraint violations
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In-Class Exercise
(Taken from Exercise 5.15)
Consider the following relations for a database that keeps
track of student enrollment in courses and the books
adopted for each course:
STUDENT(SSN, Name, Major, Bdate)
COURSE(Course#, Cname, Dept)
ENROLL(SSN, Course#, Quarter, Grade)
BOOK_ADOPTION(Course#, Quarter, Book_ISBN)
TEXT(Book_ISBN, Book_Title, Publisher, Author)
Draw a relational schema diagram specifying the
foreign keys for this schema.
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